#Obtuse Triangle

Types of Triangles A) Based on SIDES 1. Equilateral Triangle: All sides are equal. All angles are 60°. Real-life: Road signs, yield sign. 2. Isosceles Triangle: Two sides equal, two equal angles. Real-life: Roofs, kites, dresses. 3. Scalene Triangle: No equal sides, no equal angles. Real-life: Stretched tents, irregular shapes. B) Based on ANGLES 1. Acute Triangle: All angles less than 90°. 2. Right Triangle: One angle is exactly 90°. Real-life: Ladders against walls, ramps. 3. Obtuse Triangle: One angle more than 90°. #Triangles #typesoftriangles #schoolofmathematicsnigeria

🧐 Investigating Area Part 2! This triangle is called an obtuse triangle because one of its angles is obtuse. Students sometimes have trouble finding the height because it is outside of the triangle. In the video, I demonstrated dropping an item from the vertex to visualize the height. This visual can also work when the height is inside of the triangle - just think of it like dropping something down a deep well!

The Pythagorean theorem is often introduced for right-angled triangles, but its geometric beauty extends far beyond that special case. In an obtuse triangle, where one angle exceeds 90°, the relationship between the sides adapts in a precise and meaningful way. For triangle ABC with an obtuse angle at C, the formula becomes: AB^2 = AC^2 + BC^2 + 2·BC·CD, where CD represents the orthogonal projection of AC onto BC. This additional term accounts for the “extra stretch” created by the obtuse angle, correcting the standard Pythagorean relationship. This result is closely connected to the Law of Cosines, offering a geometric interpretation through projections rather than trigonometric functions. By visualizing the projection CD, we can clearly see how distances redistribute when angles expand beyond 90°. In this animation, we explore this idea step by step, transforming abstract algebra into intuitive geometry. Understanding this extension helps build a deeper foundation in triangle geometry, vector projections, and advanced mathematical reasoning. Perfect for students, teachers, and anyone curious about how classical theorems evolve in broader contexts. #mathematisa #Pythagoras #geometry #fyp

📞 Geometry shortcuts exist! Call Bright Icon Tutor or DM for enrollment! 📐 RIGHT TRIANGLE AREA HACK Normal: Area = ½bh 😴 Secret: Area = x × y 🤯 How: Draw incircle Find where it touches hypotenuse Split point creates x and y Multiply! This works because of: ✅ Incircle properties ✅ Right triangle geometry ✅ Visual rearrangement proof Appears in: 🎯 HSC/VCE Geometry 🎯 IGCSE/GCSE Mathematics 🎯 IB Mathematics 🎯 Competition math (AMC, AIME) At Bright Icon Tutor: ✨ Geometry shortcuts ✨ Visual proofs ✨ Exam strategies ✨ Competition prep 📲 Master geometry! 💬 DM "AREA" 🔗 Link in bio Bright Icon Tutors — Geometry simplified. #geometryhack #mathshortcut #onlinetutor #mathtutor #atarprep #hscmaths #vcemaths #igcsemath #ibmath #geometryproofs #trianglearea #visuallearning #mathhelp #stemeducation #mathematicseducation #australianeducation #uaeeducation #dubaitutor #sydneytutor #geometryhelp #mathtricks #onlinelearning #privatetutor #extensionmaths #mathconcepts #educationalcontent #geometricproofs #BrightIconTutor #learngeometry #stemsuccess

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🔵 𝗧𝗵𝗲 𝗦𝗲𝗰𝗿𝗲𝘁 𝗖𝗶𝗿𝗰𝗹𝗲 𝗜𝗻𝘀𝗶𝗱𝗲 𝗘𝘃𝗲𝗿𝘆 𝗧𝗿𝗶𝗮𝗻𝗴𝗹𝗲! 🔺 What if we told you that 𝗲𝘃𝗲𝗿𝘆 𝘁𝗿𝗶𝗮𝗻𝗴𝗹𝗲—no matter how it looks—𝗵𝗶𝗱𝗲𝘀 𝗮 𝗽𝗲𝗿𝗳𝗲𝗰𝘁 𝗰𝗶𝗿𝗰𝗹𝗲 within? 🎯 That’s the power of the 𝗡𝗶𝗻𝗲-𝗣𝗼𝗶𝗻𝘁 𝗖𝗶𝗿𝗰𝗹𝗲! It always passes through: ✅ The midpoints of each side ✅ The feet of all three altitudes ✅ The midpoints between each vertex and the orthocenter 📐 It’s pure 𝗴𝗲𝗼𝗺𝗲𝘁𝗿𝗶𝗰 𝗺𝗮𝗴𝗶𝗰—and a beautiful pattern seen in 𝗲𝗻𝗴𝗶𝗻𝗲𝗲𝗿𝗶𝗻𝗴, 𝗽𝗵𝘆𝘀𝗶𝗰𝘀, 𝗮𝗻𝗱 𝗱𝗲𝘀𝗶𝗴𝗻 too! 💭 Did you know triangles had this hidden masterpiece? 🎥 Credit: @reason4math (TikTok) #NinePointCircle #GeometryMagic #TriangleSecrets #MathIsBeautiful #STEMLearning #MathematicsInNature #MathInRealLife #HiddenPatterns #3iEducation #MathLove

Orthocentre explained in 40 seconds 📐 In an acute triangle → inside In a right triangle → at the right angle In an obtuse triangle → outside Three altitudes. One intersection point. Pure geometry precision. Save this for exams ✅ Comment “ORTHO” if you understood 🔥 #Orthocentre #Geometry #Triangles #Altitudes #MathsConcept #Class9Maths #Class10Maths #JEEPreparation #MathReels #LearnMath #StudyGram #CBSE #ICSE #MathShorts

Pythagorean theorem from a (semi) circle! This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the semicircle and Thales triangle theorem. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. This animation is based on a proof due to Michael Hardy from the November, 1986 issue of The College Math Journal (https://doi.org/10.2307/2686255). To buy me a coffee, head over to https://www.buymeacoffee.com/VisualProofs Thanks! For other proofs of this same fact check out the following playlist: https://youtube.com/playlist?list=PLZh9gzIvXQUvlRlnYryejWGHYQquM92rB&si=o_im7-_NHp1zhkcD #mathshorts #mathvideo #math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof To learn more about animating with manim, check out: https://manim.community

Neat and simple proof. Just drive along 🚗 . . . This visual proof shows why sum of exterior angles of any polygon is always 360° - no matter its size. Learn math the Cuemath way. Link in bio. #math #learning #triangles #polygons #angles #school #teacher #parenting #teaching #cuemath #maths #proof

The relationship between the sine and cosine of an angle is a fundamental rule of geometry derived from the properties of a right-angled triangle. This specific proof demonstrates why the square of the sine of an angle plus the square of the cosine of that same angle always equals exactly one. The unit circle foundation To visualize this proof, imagine a circle with a radius of exactly one unit centered on a coordinate grid. This is called the unit circle. If you draw a line from the center of the circle to any point on its outer edge, the length of that line is always one. Defining the coordinates When you draw that radius, it forms an angle with the horizontal axis. From the point where the radius touches the circle, you can drop a vertical line down to the horizontal axis, creating a right-angled triangle. In this triangle: 1. The slanted side, or hypotenuse, is the radius of the circle, which is one. 2. The vertical side represents the sine of the angle. 3. The horizontal side represents the cosine of the angle. The Pythagorean connection Because this is a right-angled triangle, it must follow the Pythagorean theorem. That theorem states that the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse). In our specific triangle, the two shorter sides are the sine and the cosine. The hypotenuse is the radius of the circle, which is one. Therefore, when you square the sine and add it to the square of the cosine, the result must be the square of one. Since one multiplied by itself is still one, the sum is always exactly one. Universal application This proof works for any angle, whether it is 20 degrees, 45 degrees, or any other value. No matter how you rotate the radius around the circle, the triangle it forms will always have a hypotenuse of one. The vertical and horizontal sides will change in length, but their relationship will always remain tethered to that fixed radius. For educational purpose only, kindly DM for copyright infringement.

🌀 THE PENROSE TRIANGLE: A 3D Illusion From a 4D Truth? 📐 Don't blink! Stare at this object for just three seconds and your eyes will start to glitch. This is the Penrose Triangle, an "impossible object" that has melted countless minds. Here is the science behind this brain-bending illusion: 1. The Impossible Design The Look: At first glance, it appears to be a solid 3D triangle with every edge perfectly square and every corner neat. The Twist: Its right angles somehow form a closed triangle, creating a shape that contradicts the laws of Euclidean geometry. The Confusion: Your brain simply can't process what is "near" and what is "far," leading to a visual paradox. 2. Dimension and Perspective Mathematical Space: While it cannot exist in real three-dimensional space, it can exist in special mathematical spaces—or even 4D space. The Perfect Viewpoint: In our 3D world, the illusion only works from one perfect viewpoint. * Collapsing the Trick: As soon as you shift your angle even slightly, the illusion collapses, revealing that the object is actually made of disconnected or twisted pieces. [Image showing the Penrose Triangle broken into segments to reveal the trick] 3. Pure Brain Trickery The Penrose Triangle is a masterpiece of brain trickery. It proves that what we see isn't always reality—it's just our brain's best guess based on perspective! #penrosetriangle #opticalillusion #braingames #geometry #mindbending #3dart #physicsfun #reels #techbehindthings #thepartyouneversee

Visual Proof of Sin(α+β) Formula Using Triangle Area | Step-by-Step Geometry Explanation #maths #trigonometry #mathematics #jeemains Did this visual proof help you understand sin(α+β) better?