Right Triangle Altitude Theorem Quizzes & Tests | Similarity & Geometric Mean

Description

Assess the Right Triangle Altitude Theorem, geometric mean, and right triangle similarity with three quizzes and two complete tests. These high school geometry assessments include print-ready PDFs, editable PowerPoint files, and complete answer keys with work shown.

Students work with the three similar triangles formed when an altitude is drawn to the hypotenuse of a right triangle. Questions progress from identifying corresponding parts and writing proportions to applying the altitude and leg relationships to find missing lengths.

Skills Assessed
Finding geometric means
Solving equations involving geometric means
Identifying the three similar triangles formed by an altitude to the hypotenuse
Writing similarity statements in corresponding order
Matching corresponding sides
Writing and solving proportions
Applying the right triangle altitude relationship
Applying both right triangle leg relationships
Finding missing hypotenuse segments, altitudes, and legs
Simplifying radicals and rounding when necessary
Solving multi-step right triangle problems

Three Quiz Options
Quiz A assesses geometric mean, similar triangles, corresponding sides, and proportions.
Quiz B focuses on finding missing lengths using the altitude and leg relationships. Some questions require students to find the entire hypotenuse before solving.
Quiz C is a cumulative 10-question quiz using two complete right triangle diagrams. Students identify relationships, select equations, recognize similar triangles, and calculate multiple missing lengths.

Use the quizzes throughout instruction, as a cumulative check, for additional practice, or as review before the test.

Two 10-Question Tests
Both tests assess the same essential skills and conclude with a Blackbeard’s Treasure application. Students calculate four connected distances—the entire hypotenuse, altitude, and both legs—and use their answers to complete the numbered treasure-chest dials.

Test A: Independent Application
Students draw and identify the three similar triangles, set up their own proportions, and apply the altitude and leg relationships independently.
Test B: More Structured
The three triangles are provided separately, students complete the similarity statement, and selected relationships are supplied to help organize the calculations. Students must still interpret the diagrams, substitute correctly, and complete each calculation.

Test B may be used as a scaffolded option, accommodated assessment, alternate test form, make-up test, or reassessment.

What’s Included
Quiz A and answer key
Quiz B and answer key
Quiz C and answer key
Test A and answer key
Test B and answer key
Complete answer keys with work shown
Print-ready PDF files
Editable PowerPoint files
Teacher Use Guide

The editable PowerPoint files allow you to adjust wording, measurements, directions, or layouts to fit your students and pacing. For the most reliable formatting, edit the files in Microsoft PowerPoint. Conversion to Google Slides or other programs is not recommended because equations, diagrams, and fonts may shift.

Need Instruction and Practice First?
The corresponding Right Triangle Altitude Theorem lesson includes lesson notes, practice, a quiz, geometric mean, right triangle similarity, and the altitude and leg relationships.

This lesson is also included in my complete Right Triangles and Trigonometry Unit, which covers:
Similar right triangles
The Right Triangle Altitude Theorem
Special right triangles
Right triangle trigonometry
The Law of Sines
The Law of Cosines

Choose the individual lesson if you need instruction and practice for this topic, or the complete unit for a full sequence of right triangle and trigonometry lessons.