Geometry For Absolute Geniuses

Can You Solve This Geometry Puzzle Without Using Trigonometry? 📐 In today's video, we tackle a beautiful right triangle problem that looks simple on the surface but requires a clever construction to solve elegantly. We are given a right triangle ABM with a vertical side length of 1, a point C on the base such that angle ACM = 75°, and a segment BC with a length of 2. Our goal? Find the exact value of angle B (Angle X). While many would reach for their calculators or complex trig identities, we’re doing things differently. By constructing an auxiliary equilateral triangle and exploring congruent and similar triangles, we’ll uncover the answer using pure geometric logic. In this video, you’ll learn: How to use auxiliary constructions to simplify complex problems. The power of equilateral and isosceles triangle properties. How to identify congruent and similar triangles to find missing side lengths and angles. Timestamps: 0:00 - The Problem Setup 0:34 - The "Special" Construction 2:04 - Identifying Similar & Congruent Triangles 3:55 - The Remarkable Final Discovery 5:23 - The Solution Did you manage to find the answer before the final step? Let me know your method in the comments! If you enjoyed this "Math Booster," don't forget to like and subscribe for more geometry puzzles and mathematical insights.