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Theater Set Shop: Why the Right-Angle Test Works

Students explain a similarity proof of the Pythagorean Theorem and its converse while checking theater set braces and seating layouts.

Grade 8MathInteractive · Printable

Aligned to8.G.B.6

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
13 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students explain how triangle similarity proves the Pythagorean Theorem.
Students explain how a constructed right triangle and SSS congruence prove the converse.
Students distinguish the theorem from its converse when checking theater designs.

How to use

Work through the similarity sketch together, then have students complete the proof and review the theater designs independently. Ask students to identify what is known before choosing a theorem.

Curriculum

Common Core standard covered

8.G.B.6

Explain a proof of the Pythagorean Theorem and of its converse.

Preview

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Theater Set Shop: Why the Right-Angle Test Works

Use similarity to prove a theorem, then justify its converse.

1. Prove the Set Shop's Rule

Read the sketch and proof notes. Choose statements that follow from similarity, not from the theorem you are proving.

The theater club uses right-triangle braces. Before using a² + b² = c², the crew studies why it is true. The graph locates the points for a right triangle ABC with its right angle at C. On the graph, add segments AD and CD to complete the proof sketch. Segment CD is perpendicular to hypotenuse AB, and D lies between A and B.

For the general proof, use AC = b, BC = a, AB = c, AD = p, and DB = q. Thus p + q = c. The sketch is one example; the proof applies to any right triangle with an altitude to its hypotenuse.

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