Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

Grade 8

The Concept of CongruenceModule two

TOPIC D

The Pythagorean Theorem

INFORMAL PROOF OF THE PYTHAGOREAN THEOREM

Lesson fifteen

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen

Concept DevelopmentPythagorean Theorem: If the lengths of the legs

of a right triangle are and , and the length 𝑎 𝑏of the hypotenuse is , then 𝑐 𝑎2 + 𝑏2 = 𝑐2.

Given a right triangle ABC with being the 𝐶vertex of the right angle, then the sides AC and BC are called the legs of ∆ABC, and AB is called the hypotenuse of ∆ABC.

Basic Geometry Facts1. Congruent triangles have equal areas.

2. All corresponding parts of congruent triangles are congruent.

3. The triangle sum theorem. ( sum of )∠ △ a. For right triangles, the two angles that

are not the right angle have a sum of 90°. ( sum of rt. )∠ △

Basic Geometry Facts

EXAMPLE TWO

Determine the length of the hypotenuse of the right triangle.

EXERCISES 1-3Determine the length of the hypotenuse of the right triangle.

EXERCISES 4-5Determine the length of the hypotenuse of the right triangle.

Lesson Summary

APPLICATIONS OF THE PYTHAGOREAN THEOREM

Lesson sixteen

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen

EXAMPLE ONE

EXAMPLE TWOSuppose you have a ladder of length 13 feet. Suppose that to make it sturdy enough to climb, you must place the ladder exactly 5 feet from the wall of a building. You need to post a banner on the building 10 feet above the ground. Is the ladder long enough for you to reach the location you need to post the banner?

EXAMPLE THREEGiven a right triangle with a hypotenuse of length 15 units and a leg of length 9, what is the length of the other leg?

EXERCISE 1

EXERCISE 2

EXAMPLE FOUR

EXAMPLE FIVE

Given a rectangle with side lengths of 8 cm and 2 cm, as shown, what is the length of the diagonal?

EXERCISE 3

Find the length of the segment AB, if possible.

EXERCISE 4

4. Given a rectangle with dimensions 5 cm and 10 cm, as shown, find the length of the diagonal, if possible.

EXERCISE 5 & 6

A right triangle has a hypotenuse of length 13 in. and a leg with length 4 in. What is the length of the other leg?

Find the length of in the right triangle below, if possible. 𝑏

Lesson Summary

Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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