grade 8 the concept of congruence module two. topic d the pythagorean theorem
TRANSCRIPT
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.
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen
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. )∠ △
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen
Basic Geometry Facts
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen
EXAMPLE TWO
Determine the length of the hypotenuse of the right triangle.
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen
EXERCISES 1-3Determine the length of the hypotenuse of the right triangle.
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen
EXERCISES 4-5Determine the length of the hypotenuse of the right triangle.
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen
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
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
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?
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
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?
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
EXERCISE 1
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
EXERCISE 2
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
EXAMPLE FOUR
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
EXAMPLE FIVE
Given a rectangle with side lengths of 8 cm and 2 cm, as shown, what is the length of the diagonal?
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
EXERCISE 3
Find the length of the segment AB, if possible.
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
EXERCISE 4
4. Given a rectangle with dimensions 5 cm and 10 cm, as shown, find the length of the diagonal, if possible.
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
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
NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen
Lesson Summary