11/9/2023 0 Comments Lady in blue yacht owner![]() It’s important to keep your boat in top condition to ensure that your voyages run smoothly and you can make the most of your time out on the water. We also provide yacht repair and maintenance services for existing yacht owners in Southeast Asia. Our representatives have years of experience completing all the paperwork, surveying and sea trials that the ownership transfer of a yacht requires, so you can be confident that your yacht is in good hands. Our boat brokerages in Thailand and Singapore are particularly active in the chartering business. We handle all the day-to-day activities that chartering entails so you can be an absentee boat owner and still reap all the benefits that chartering provides. Chartering allows you to reduce or even eliminate the maintenance costs and other expenses that go hand in hand with boat ownership. You can enjoy many benefits by allowing us to charter your boat out for you. We offer a full range of charter services that allow you to treat your love of yachting as your passion and a great investment. And our helpful staff are happy to help you consider the best options for your next yachting excursion. No matter what kind of seafaring experience you’re looking for, we have a quality watercraft for you. These quality brands offer everything from runabouts and inflatables all the way up to luxury superyachts. Our new yachts for sale represent some of the finest quality brands, including Burgess, Jeanneau, SACS, and Princess Yachts. Our many offices allow us to offer you the best sales, service and charters within the Southeast Asia region. We have luxury yacht brokerage locations in Singapore, Malaysia, the Maldives, and Indonesia, and four in Thailand. ![]() ![]() YACHTS FOR SALE IN ASIA | BOAT LAGOON YACHTINGĪt Boat Lagoon Yachting, we offer new and pre-owned luxury yachts for boating enthusiasts across Southeast Asia.
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11/9/2023 0 Comments Little voice e08![]() Howard trying to be a supportive person carried Candice out of the situation. Their actions had consequences inside and outside of the Big Brother house. ![]() Now for both GinaMarie and Aaryn it'll be interesting to see how they'll react at themselves when they get out of the house. I think it was childish how GinaMarie and Aaryn started to bully against Candice. This blew up when it didn't need to, yet being stuck in a house for three weeks starts to wear people and for GinaMarie it showed. In all fairness, nobody has ownerships to any of the beds in the house, but one would think people have common courtesy. However Jessie wasn't having it and calmly asked if Kaitlin nor Jeremy weren't having. Emotions On High And Tempers FlareĪ few hours after the HOH competition, Aaryn decides to find a bed that she'll want to sleep in now that she's been dethroned from power. It was good to see that studying pays off. But the HOH competition was down to the wire, where they had to go to a second tire breaker, which I can not remember ever happening in the past seasons. Sadly for Aaryn, Jeremy, GinaMarie and Kaitlin they ended up falling short to the Mom Squad as Helen won HOH. While Jeremy was in shock but knew that this was a game and had to move on. Kaitlin badgering Jessie was a bit unnecessary especially right before the competition but Kaitlin, like GinaMarie and Aaryn felt betrayed and wanted answers. Not surprised the house slowly figured out who the fourth vote was but it also let to some confrontations. Which I commend Spencer in doing, but it left Howard in a tough spot. Spencer was upfront to Howard that he had switched his vote and said it's about winning the game. However GinaMarie also had some choice words to the houseguest that voted out Nick, while Aaryn was the little voice fueling the fire. I did find it interesting that Aaryn was their to comfort her and try to get her back in the game to fight for HOH. Live Feeders know that this happened for several hours after the eviction. It's interesting to see how close of a bond someone can have with other houseguests but GinaMarie was crying a river of tears. Poor GinaMarie, sad to see her crush of only three weeks leave the house. ![]() Ironic for Aaryn to say she's in the "minority" when she has been on blast about racial stereotypes. The "CEO" has left the building thanks to two of its members siding with the Mom Squad and the "majority" of the house. Love to hate or hate to love, it's getting viewers to watch the show. As the saying goes, "We're not all cookie cutter," and this applies for Big Brother. Now granted, for Big Brother it's a game show but nonetheless we're watching real people. We're watching real-life people and how they act on a daily basis. It is good to remember what reality TV is. All the networks have done this and not just for reality TV. This wasn't the first time CBS has needed to do this - nor will it be the last. In case you missed it, at the very beginning of the show CBS reiterated their statement about the game, the houseguests and where CBS stood. By Mark discretion is advised, thanks CBS for that reminder. 11/9/2023 0 Comments Jpegmini pro![]() Free trials of both versions can be downloaded here. The package also includes a plug-in for Adobe Lightroom. Files from cameras up to 60MP can be handled files and batch files are processed at up to five times the speed of JPEGmini. JPEGmini Pro runs on Mac but a Windows version is due soon. The starter version handled files up to 28MP and is perfect for most cameras up to DSLR standard. There are three versions of JPEGmini available. Without further ado, here are the details for JPEGmini Pro 3.3 : Our JPEGmini app will now provide one place for both image and video optimization. I tested the software on a selection of my own image files and I have to admit I couldn’t tell the difference between the full-fat JPEG files and the ‘diet’ versions that JPEGmini created, even when viewed at 100% on screen. Files up to 60MP can be crunched by JPEGmini Pro, which will please photographers shooting on medium-format digital cameras. JPEGmini comes as a standalone piece of software with a simple drag-and-drop interface and there’s also a Lightroom plug-in available with the Pro version. Desktop (Mac & PC) - Unlimited 28MP photos Learn More JPEGmini Pro. Don't have JPEGmini Pro Suite yet Get it now JPEGmini - The Photo Optimization Tool Trusted by Tens of Thousands Image Perfectionists. SEEMS YOUR PHOTO LOST SOME WEIGHT Choose Your JPEGmini Version JPEGmini. Clients include Netflix, which uses the software to reduce image sizes and bandwidth use across its global systems. Free download for existing JPEGmini Pro Suite users, please enter your purchase email below and we'll send you the instructions. According to Beamr, the developer of JPEGmini, around 250 million image files each day are squashed via JPEGmini Server. JPEGmini Pro is aimed at professional photographers as well as websites that want to create images that will load as quickly as possible, something that’s increasingly important in an age of cellular communications. On smaller image files the savings are a little lower at a still very useful 30-50%. The JPEGmini Pro Suite Photo Optimization Software is a photo resizing application designed to reduce overall file sizes without sacrificing image quality. What does this mean in practice? On larger images it’s possible to reduce the file size by up to 80% or a factor of 5. In other words, JPEGmini analyses each image and then sacrifices unnecessary data points without harming the integrity of the image. JPEGmini does this by creating a single quantization matrix for an entire image so that it’s compliant with the baseline JPEG standard. You now have the full version of JPEGmini Pro v3.3.0.0 installed on your PC.This is where JPEGmini comes in: a new piece of software that offers to save image files in the JPEG baseline standard but with a much smaller footprint and no greater loss of image quality than regular JPEG compression. JPEGmini Pro promises that their proprietary algorithm can dramatically reduce the size of JPGs with no discernible loss in quality.Run JPEGmini Pro.msi and install the software.If you don’t know how to extract, see this article. This might take from a few minutes to a few hours, depending on your download speed. So, if you were on the fence about purchasing either the Hasselblad H6D or the Phase One XF, or maybe both, but couldn’t because we previously only optimized photos up to 60MP, you’re good to go now. Click on the download button(s) below and finish downloading the required files. JPEGmini Pro now supports resolution of up to 128MP covering most commercial cameras, including medium format and panoramas.How to Download and Install JPEGmini Pro v3.3.0.0 Operating System: Windows 8 and higher.JPEGmini Pro v3.3.0.0 System Requirements Reduce image file size without compromising quality.You can add more photos to your cloud storage account, flash drives, and other areas where you would normally store photos. For those with an image-intensive website, your web pages will load faster, improving user experience, monetization and SEO.Ĭut your image storage and delivery costs when optimizing your images with JPEGmini. Smaller image file sizes allow you to upload and download your full resolution images faster. Using patented image optimization technology, JPEGmini reduces the file size of your photos significantly (up to 80%), while preserving their full resolution and quality. ![]() You can upload Hi-Res photos faster, save tons of hard drive space, improve customer viewing experience and make your website faster. Get the smallest image file size without compromising quality or changing your workflow. Everyone at JPEGmini is excited to share our new update with our creators. After research and listening to feedback from users, the JPEGmini team worked hard to enhance features for a better experience. JPEGmini Pro is finally out with our 3rd new upgrade. 11/9/2023 0 Comments Epic pass lodging![]() that Vail Resorts acquired from Peak Resorts. Pass Holders can receive the 20 savings by presenting their pass at the register, logging into their account to book online, or by verifying their pass number. “We are very pleased to see the growth in visitation this season, and in particular that it primarily occurred during off peak periods… For the season-to-date period ended April 30, 2022, compared to the season-to-date period ended May 5, 2019, visitation on weekday and non-holiday periods increased approximately 8% while visitation on weekend and holiday periods decreased approximately 3%, excluding Peak Resorts visitation in both periods,” she said, referring to resorts such as Mount Snow, Vt. Benefits at Perisher, Falls Creek & Hotham. Military Epic Pass or Infant Epic Australia Pass. Lynch also noted that there is a trend toward weekday and off-peak visits. Save on lodging, rentals, transportation and more - just by being a pass holder Explore other deals and discounts at your favourite resorts across North America to get the most value out of your pass. Of course, if you look at an average of 40 resorts across the globe, lumping in Jack Frost, Pa., say with Stowe, Vt. All of this highlights that there is considerable opportunity to continue to grow the overall industry and skier visits outside of peak periods,” she said in a release. “Despite the growth in overall visits this past season, very few of our resorts even approached their historical maximum daily visitation, as our resorts averaged only 1 day this season exceeding 95% of their historical peak daily visitation and only 6 resorts had more than 1 day above that level, excluding the recently acquired Seven Springs Resorts. CEO Kirsten Lynch claimed the numbers show there is still room for growth. While many skiers at Vail Resorts’ three Vermont ski areas complained of long lines, traffic and crowding this past season (see Why Is Everyone So Angry At Vail Resorts?). Vail Resorts reported earning a net income of $372.6 million for the third fiscal quarter of 2022 compared to a net income of $274.6 million in the same period in the prior year. The company also increased the percentage of its visitors who use a pass, versus a day ticket, to 72%, up from 60% in 2021-22.Īll that translates into more than a 35% increase in revenue. Epic Pass Holders will receive one free day of skiing for each. This takes into account Vail Resort’s 2022 purchase of Seven Springs Resort in Pennsylvania. Is there a hotel or lodging requirement to receive benefits at Verbier 4 Valles Yes. On June 9th Vail Resorts (which owns Stowe, Okemo and Mount Snow) released its quarterly earnings reports and guess what? Already, the number of Epic Passes sold for the 2022/23 season is up by 9% in units sold over last year. If you thought the boom in skiers and riders using Vail Resort’s Epic Pass had peaked, think again. 11/9/2023 0 Comments Jam jar wine![]() When Pinotage is blended with other red varieties, like Cabernet Sauvignon, Merlot, Syrah or Pinot Noir (all commonly vinified alone as well), it is often labeled as a “Cape Blend.” Chenin Blanc (locally known as “Steen”) dominates white wine production, with Chardonnay and Sauvignon Blanc following close behind. Pinotage, a cross between Pinot Noir and Cinsault, is the country’s “signature” grape, responsible for red-fruit-driven, spicy, earthy reds. South Africa’s wine zones are divided into region, then smaller districts and finally wards, but the country’s wine styles are differentiated more by grape variety than by region. Similarly, cooler, high-elevation vineyard sites throughout South Africa offer similar, favorable growing conditions. But the Benguela Current from Antarctica provides brisk ocean breezes necessary for steady ripening of grapes. Wine production is mainly situated around Cape Town, where the climate is generally warm to hot. A more fun style than your typical Shiraz, this fresh, fruity, semi-sweet wine displays aromas and flavors of ripe, juicy berries with dark chocolate undertones. Today, however, South Africa is increasingly responsible for high-demand, high-quality wines-a blessing to put the country back on the international wine map. Since then, the South African wine industry has experienced some setbacks due to the phylloxera infestation of the late 1800s and political difficulties throughout the following century. The country has a particularly long and rich history with winemaking, especially considering its status as part of the “New World.” In the mid-17th century, the lusciously sweet dessert wines of Constantia were highly prized by the European aristocracy. When Pinotage is blended with other red varieties, like Cabernet Sauvignon, Merlot, Syrah or Pinot Noir (all commonly vinified alone as well), it is often labeled as a “Cape Blend.” Chenin Blanc (locally known as “Steen”) dominates white wine production, with Chardonnay and Sauvignon Blanc following close behind.With an important wine renaissance in full swing, impressive red and white bargains abound in South Africa. By entering and using this site, you agree to our Legal & Policies. By clicking 'yes' you affirm you are at least 21 years old. ![]() Pinotage, a cross between Pinot Noir and Cinsault, is the country’s “signature” grape, responsible for red-fruit-driven, spicy, earthy reds. Hey there, Are you over 21 You must be at least 21 years old to view this site. Jammy, sweet and delicious, which is what it wants to be. South Africa’s wine zones are divided into region, then smaller districts and finally wards, but the country’s wine styles are differentiated more by grape variety than by region. Friendly, sweet style, with cherry pie, vanilla and red licorice notes. Wine production is mainly situated around Cape Town, where the climate is generally warm to hot. With an important wine renaissance in full swing, impressive red and white bargains abound in South Africa. 11/9/2023 0 Comments Kids new year countdownsBegin counting backwards and when you reach the end of the countdown shout “Happy New Year’s!” and shake the bag so that the drawstrings open and all of the confetti and balls drop down. When ready for the countdown stand over a balcony or hold the bag above the littles. 5-4-3-2-1 Countdown the New Year with this simple paper plate countdown craft found on JDaniel4’s Mom. Practice telling the time as you countdown with these paper plate countdown clocks as seen on Buggy and Buddy. Pull the draw strings loosely shut but do not tie the drawstrings on the garbage bag. Laugh as a family with these New Year’s Eve Mad Libs which can be printed from Happiness is Homemade. Blow up smaller balloons and add these to the bag as well (or add the ball pit balls if using these instead). Stuff the paper and tissue paper into the garbage bag. Enjoy a special video countdown and Ginger Ale Toast to ring in 2023. Celebrate the New Year’s with mouthwatering food, thrilling arcade games, and fun for the whole family. Repeat ripping with the tissue paper as well. Dave and Buster’s, 625 Atlantic Avenue, Boerum Hill. This new years countdown for kids is not only filled with fun new years eve games, new years eve crafts, and engaging new years eve countdown activities. The more pieces you use the bigger the confetti drop (and the bigger the clean-up). Repeat this with as many colors and pieces of construction paper as desired (I used 8 pieces). Give your child construction paper in all different colors and show them how to rip up the large sheets into smaller pieces. ![]() This is a great activity for working on toddler fine motor and ripping skills. Blue Man Group Chicago New Years Eve Performances at Briar Street Theatre Bubble Bash New Years Eve at DuPage Childrens Museum Countdown to Fun at. Small Balloons (works best) OR ball pit balls.Construction paper in all different colors.Scroll down for more directions on how to create a New Year’s Confetti Ball Drop and New Year’s Eve hats. It’s a super simple activity and uses items from around the house. While it didn’t last long it was a loved activity and we proceeded to have to pick up and repeat the drop over and over. The littles shouted “Happy New Year!” and danced around in the confetti. Watch TV and mark off what you see on your bingo card (fireworks, balloons, 2022, etc.). We counted down and let our confetti ball drop open over the balcony. This is great for all ages Print out bingo sheets online or design your own for a festive way to get kids involved with the ball drop celebrations. We put the PBS kids New Year’s Countdown on youtube. ![]() Then when it was close to Noon on the 31st we put on our hats and got ready for the countdown. We created the following “New Year’s” headbands and confetti ball drop together. We started our party in the late morning with all our favorite snacks and special “bubble juice (sparkling grape juice).” Then my mini and I started crafting. Since the minis stick to a pretty solid bedtime we didn’t want them staying up until midnight (nor did we think we were able to stay up that late). Are you looking for fun New Year’s Eve Countdown Activities to do with toddlers at home? This New Year’s we were looking for something fun and different to do being stuck at home. 11/9/2023 0 Comments Final draft latest version![]() Ulysses' price has gone up in recent years and now costs $49.99 per year or $5.99 per month (which works out to about $72 per year). Scrivener, for example, costs $49 for the Windows or macOS app and $19.99 for the iPhone and iPad apps. Most other writing apps charge less for their desktop editions, but more for their mobile apps. It has many of the same tools as Final Draft, including index cards, collaboration, and the ability to upload PDFs of scripts and have them converted to an editable script form. Similar to Final Draft, Fade In focuses on screenplay writing. Frankly, it's more expensive than any other writing app I've reviewed.įade In, for example, costs only $79.95, and it's available for all major platforms and Linux. How Does Final Draft's Price Compare?įinal Draft's $249 sticker price might induce sticker shock for some. It's worth adding the mobile app if you're the type of writer who prefers to jot down ideas and notes directly into your scripts rather than in a separate note-taking app. The iPad and iPhone apps sell separately, and you can access your scripts through it when you save them to Dropbox or iCloud (you can also get them via email, which is a less elegant solution). If you buy the app, you get a license code via email that you enter the next time you launch it. You can install Final Draft and try it for 30 days without providing a credit card. You buy the software once and own it for life, though you will have to pay for upgrades once every few years if you want them. Mind you, these are one-time fees and not recurring subscription costs. Additionally, there are discounts for students, and sometimes the app goes on sale for around $199. ![]() The desktop software is not cheap, but the good news is that with a purchase, you can install Final Draft on two machines. How Much Does Final Draft Cost?įinal Draft is available for macOS and Windows ($249), with a version called Final Draft Mobile available as an iPad app and an iPhone app (both for $9.99). They range from the practical, such as a spellcheck in the Beat Board, to more stylistic, such as having ScriptNotes appear as flags on the page which open when you click them. I tested this feature and it worked very well, with only minimal cleanup needed.Īs mentioned, the Beat Board, ScriptNotes, and Outline Editor all received updates as well. When you upload PDFs of screenplays and other scripts, Final Draft interprets the formatting, too. The PDF import tool lets you upload a PDF and convert it to editable text. It works much like other apps that offer Track Changes, with different colors tracking changes of different collaborators, the ability to accept and reject changes individually or globally, and so forth. Track Changes primarily makes the collaboration options in Final Draft better. Focus Mode lets you minimize distractions while working on your script. Three features worth highlighting are 1) Focus Mode, 2) Track Changes, and 3) a PDF import tool. When you need help organizing and formatting large amounts of content, however, Final Draft, Scrivener, and Ulysses are the best writing apps on the market.Īs of version 12, Final Draft has a few new and noteworthy features, as well as significant improvements to the Beat Board, ScriptNotes, and the Outline Editor. Beyond those, there are wonderful, inexpensive writing apps that are perfectly suitable for shorter and less structured content, such as articles and marketing copy. Our favorites among them are Scrivener, which is available for both Windows and macOS and the Mac-only Ulysses. If you're not primarily a screenwriter, other apps are worth investigating because they have some advantages for novelists and book authors. Final Draft is a PCMag Editors' Choice winner for screenwriting software and one of the best apps for writers in general. Among writing apps, Final Draft is one of the most expensive products you can buy, but it's worth the price and sells for a one-time fee rather than as a recurring subscription. A Beat Board feature replicates the old notecard approach to arranging scenes, and a Story Map helps keep the story on target for pacing and script length. ![]() It compiles lists of characters and scene locations automatically. The app has smart auto-suggestions for formatting your work to industry standards. Professional screenwriters use Final Draft, and you should too, if that's your field. Best Hosted Endpoint Protection and Security Software. But the spirit impersonating her mom convinces her that her dad is actually one of the evil spirits trying to harm her and Mia stabs him.Renee Zellweger delivers one of the best performances of her career in this underrated rom-com, and the centerpiece is an epic monologue that lays out a jaw-dropping twist about the background and motivations of her character, self-help author Barbara Novak. Mia's father eventually ends up showing her her mom's suicide note, which he'd been hiding from her in an attempt to protect her. Sophie Wilde as Mia in Talk to Me Matthew Thorne-A24 ![]() The evil spirit pretending to be her mom tells her that she's right about her not committing suicide and that if Riley dies, she will take care of him on the other side instead of letting him suffer how he is currently. When Mia's dad found her mom's body, she had been clawing at their bedroom door trying to get help, leading Mia to believe that her mom didn't commit suicide and instead took too many pills accidentally. Mia also uses the hand on her own to try to talk to her mom, who died after taking too many sleeping pills. When this doesn't seem to work, Mia asks a spirit to show her the spirit world, where she sees Riley being endlessly tortured by a gruesome, churning mass of lost souls. Mia has the idea to try to close the door on Riley's behalf by lighting the candle, placing the hand in Riley's, saying "talk to him," and then blowing out the candle on her own. To make matters worse, every time Riley comes to, the spirits take hold and try to kill him so they can claim him forever. With Riley catatonic and near death in the hospital, Mia begins experiencing increasingly terrifying encounters with the dead. They finally get the hand away and call emergency services. ![]() Jade rushes back in just in time to throw her hand in between Riley's head and the side of the desk on which the spirit is attempting to deliver the killing blow. As the others fight to wrestle the hand from him, he reaches up and tries to pull out his own eyeball before flying across the room. Suddenly, something shifts and Riley begins violently slamming his head onto the table in front of him. The spirit enters Riley and begins talking to Mia as if it's her late mother, leading Mia to let the possession go on for much longer than 90 seconds. Joe Bird as Riley in Talk to Me Matthew Thorne-A24 With Jade gone, Mia gives in and says that Riley can try it out, but only for 60 seconds. Riley eventually begs for a turn but Jade forbids it before leaving the room. At the next group get-together, everyone takes turns getting high on the thrill of the hand and filming the ghostly encounters for social media. ![]() Mia broke the rules-and now must face the consequences. The group is eventually able to rip the hand from Mia's grasp and she jubilantly emerges from her otherworldly trance. But when Joss (Chris Alosio), the hand's other keeper, tries to pry it away from Mia as the clock approaches 90 seconds, the spirit resists and time goes over. Mia performs the ritual and experiences the unmatched high of possession for the first time, channeling a spirit that takes a particular interest in Riley. 11/8/2023 0 Comments Medieval knight cartoon![]() Still, from the pioneering years of cinema in the first half of the twentieth century to the huge blockbusters of the modern day, there are more than a few of the best medieval movies that are more than worthwhile. High fantasy stories set in fictional worlds seem to be much more prevalent, but, as great as Lord of the Rings or Game of Thrones may be, they shouldn't be a complete replacement for the medieval setting. The medieval period is fertile grounds for epic tales of glory on the battlefield and romanticized reimaginings of historical events, but it seems to have fallen out of favor somewhat in recent years. From A Knight’s Tale to Henry V to The Name of the Rose, the best medieval movies are must-watches for any film fan. Medieval characters historical buildings cartoon icons set with castle ridders tent peasant king knight princess isolated vector illustration Medieval people vector illustration set, cartoon flat historical middle ages characters collection with peasant blacksmith priest laundress beggar isolated on. ![]() Medieval warriors in action poses armored knights vector characters in cartoon style. Despite the difficulties, the best medieval movies have been incredibly successful, both commercially and critically. 127,027 results for knight cartoon in all. In the background is a castle amidst a landscape with trees, hills and mountains. They require endless research to prevent them from becoming inaccurate, huge budgets to cater to the elaborate sets, costumes, and props required, and must often strike a balance between staying true to history and entertaining a modern audience. Find images exactly you are looking for from more than 86400000 of royalty-free. Vector illustration of a Medieval knight with a lance on a horse in front of an old paper scroll. ![]() The best medieval movies are difficult to do well. ![]() Instead, what if we draw a line that bisects the apex (or top) angle:Īgain we have two triangles, ΔABD and ΔACD, where the angles we want to prove are congruent are in corresponding places. But this time, suppose you didn't think of drawing a line to the middle of the base. So what if you didn't have that intuition? Well, luckily, we can prove this in another way. I think the only "tricky" part of the above proof was the intuition required to draw the line connecting A with the middle of the base. (6) ∠ACB ≅ ∠ABC // Corresponding angles in congruent triangles (CPCTC) Another way to prove the base angles theorem Given: Angle B congruent to Angle C Prove: Segment AB congruent to Segment AC Plan for proof: Show that Segment AB and AC are corresponding parts of congruent triangles. If two angles of a triangle are congruent, then the sides opposite those angles are congruent. (4) AD = AD // Common side to both triangles Converse of the Isosceles Triangle Theorem. (3) BD = DC // We constructed D as the midpoint of the base CB (2) AB=AC // Definition of an isosceles triangle So how do we show that the triangles are congruent? Easy! Using the Side-Side-Side postulate: Proof If we show that the triangles are congruent, we are done with this geometry proof. Putting these two things together, it would make sense to create the following two triangles, by connecting A with the mid-point of the base, CB:Īnd now we have two triangles, ΔABD and ΔACD, where the angles we want to prove are congruent are in corresponding places. Then, we also want ∠ACB and ∠ABC to be in different triangles, to prove their congruency. We know that ΔABC is isosceles, which means that AB=AC, so it will be good if we place these two sides in different triangles, and already have one congruent side. So let's think about a useful way to create two triangles here. Ok, but here we only have one triangle, and to use triangle congruency we need two triangles. This is the basic strategy we will try to use in any geometry problem that requires proving that two elements (angles, sides) are equal. If we can place the two things that we want to prove are the same in corresponding places of two triangles, and then we show that the triangles are congruent, then we have shown that the corresponding elements are congruent. Triangle congruency is a useful tool for the job. This problem is typical of the kind of geometry problems that use triangle congruency as the tool for proving properties of polygons. So how do we go about proving the base angles theorem? Prove that in isosceles triangle ΔABC, the base angles ∠ACB and ∠ABC are congruent. So, here's what we'd like to prove: in an isosceles triangle, not only are the sides equal, but the base angles equal as well. ![]() We will prove most of the properties of special triangles like isosceles triangles using triangle congruency because it is a useful tool for showing that two things - two angles or two sides - are congruent if they are corresponding elements of congruent triangles. In today's lesson on proving the Converse Base Angle Theorem, we'll provide a proof for both.In this lesson, we will show you how to easily prove the Base Angles Theorem: that the base angles of an isosceles triangle are congruent. Or, draw the angle bisector of A, and use the fact that it creates a pair of equal angles at A. ![]() ![]() We can draw either the altitude to the base, and use the fact that it creates a linear pair of equal right angles. And as a result, the corresponding sides, AB and AC, will be equal.Īnd just like in the original theorem, we have a choice of which line to draw. We'll do the same here, prove the triangles are congruent relying on the fact that the base angles are congruent. As a result, the base angles were congruent. There, we drew a line from A to the base BC and proved the resulting triangles are congruent. We will try to apply the same strategy we used to prove the original one - the Base Angles Theorem. When proving the Converse Base Angle theorem, we will do what we usually do with converse theorems. In triangle ΔABC, the angles ∠ACB and ∠ABC are congruent. Now we'll prove the converse theorem - if two angles in a triangle are congruent, the triangle is isosceles. We will use congruent triangles for the proof.įrom the definition of an isosceles triangle as one in which two sides are equal, we proved the Base Angles Theorem - the angles between the equal sides and the base are congruent. In today's lesson, we will prove the converse to the Base Angle theorem - if two angles of a triangle are congruent, the triangle is isosceles. |
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