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Lighthouse Restoration: Why the Measurements Work

Explain a square-dissection proof of the Pythagorean Theorem and its converse through lighthouse ladder and ramp checks.

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
14 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 a square dissection proves the Pythagorean Theorem.
Students justify the converse using a constructed right triangle and SSS congruence.
Students distinguish exact right-angle evidence from rounded measurements.

How to use

Have students connect the labeled points to complete the dissection diagram before following the proof. Discuss exact and rounded data after the final question.

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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Lighthouse Restoration: Why the Measurements Work

Use a dissection proof to justify ladder and ramp checks.

A Square-Dissection Proof

The lighthouse restoration crew makes a proof card before checking ladders and ramps. Follow how four congruent right triangles fill a square.

Complete the diagram by connecting A–B–C–D–A for the outer square and E–F–G–H–E for the inner square. Then connect A–E, B–F, C–G, and D–H. These segments divide the outer square into the inner square and four right triangles: ABE, BCF, CDG, and DAH. Each grid unit represents 1 cm.