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Library Tool Kits: A Trapezoid Proof

Use a trapezoid dissection to explain the Pythagorean Theorem, then examine its converse through library makerspace kits.

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, Matching, Circle the answer, Short answer

About this worksheet

What students practice

Students explain a trapezoid-area proof of the Pythagorean Theorem.
Students explain how a constructed right triangle and SSS congruence prove the converse.
Students distinguish numerical checks from general geometric proofs.

How to use

Use after reviewing triangle and trapezoid area. Have students complete the dissection diagram before working through the proof and reviewing the lending-kit checks.

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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Library Tool Kits: A Trapezoid Proof

Explain why a right triangle gives a square-area equality—and why the equality guarantees a right angle.

A Proof Card for the Lending Kit

The library makerspace is adding proof cards to its geometry kits. Use the diagram and the general construction to review one card.

The diagram locates the vertices of trapezoid ABCD and point E on its bottom edge. Complete the diagram by drawing segments AE, DE, and EC. Segments DE and EC divide the trapezoid into three triangles. Each grid unit represents 1 cm.For the general construction, replace AE and BC by a, and replace AD and EB by b, where a and b are positive. A, E, and B lie on one straight line. AD and BC are perpendicular to AB. The two outer triangles are congruent right triangles with hypotenuses DE = EC = c.

In the numerical diagram, AD and BC are the parallel sides of the trapezoid. Their lengths are 4 cm and 3 cm, and the distance between them is 7 cm.

What is the area of the whole trapezoid? cm²

For the general construction, which expression gives the trapezoid's area using its parallel sides and the distance between them?