Right Triangle Altitude & Leg Theorems | Geometric Mean Lesson, Practice & Quiz

Description

Teach the Right Triangle Altitude Theorem and geometric mean with this complete, teacher-ready Geometry lesson! This resource helps students understand how drawing an altitude in a right triangle creates three similar triangles, then guides them in using proportions, Corollary 1, and Corollary 2 to solve for missing side lengths and apply the geometric mean relationships in right triangles.

This lesson uses a memorable Papa Bear, Mama Bear, and Baby Bear triangle model to help students visualize the large, medium, and small similar triangles formed by the altitude. Students draw the triangles, set up proportions, and use geometric mean to solve increasingly challenging problems, making this an excellent fit for Geometry units on similarity, right triangles, and triangle proportionality.

Students will:

• identify the three similar triangles formed by an altitude in a right triangle
• use proportions to solve for missing sides
• apply the geometric mean corollaries
• solve multi-step right triangle challenge problems
• justify their reasoning using similarity relationships
• strengthen prerequisite skills for future trig concepts

This resource includes:

• guided notes / lesson pages
• structured practice problems
• a multi-variable challenge problem
• answer keys
• teacher lesson plan
• editable quiz
• bonus Pythagorean Theorem connection practice

The included challenge problem allows students to solve for multiple variables in different orders and encourages flexible problem-solving strategies, making it ideal for class discussion, partner work, stations, or early finisher extension work.

Perfect for Geometry, right triangle similarity, altitude theorem, geometric mean, and test prep review.

This resource is also in my Geometry Curriculum

Copyright ©Time Flies/Lisa Hamiter. All rights reserved by author. This product is to be used by the original purchaser only. Copying for more than one teacher, classroom or school system is prohibited. Multiple licenses are available at a discount!