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

22
Grade 8 The Concept of Congruence Module two

TAGS:

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

Page 1: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

Grade 8

The Concept of CongruenceModule two

Page 2: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

TOPIC D

The Pythagorean Theorem

Page 3: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

INFORMAL PROOF OF THE PYTHAGOREAN THEOREM

Lesson fifteen

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2

Page 4: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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.

Page 5: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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. )∠ △

Page 6: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen

Basic Geometry Facts

Page 7: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen

EXAMPLE TWO

Determine the length of the hypotenuse of the right triangle.

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

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen

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

Page 9: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen

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

Page 10: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson fifteen

Lesson Summary

Page 11: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

APPLICATIONS OF THE PYTHAGOREAN THEOREM

Lesson sixteen

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2

Page 12: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen

EXAMPLE ONE

Page 13: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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?

Page 14: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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?

Page 15: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen

EXERCISE 1

Page 16: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen

EXERCISE 2

Page 17: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen

EXAMPLE FOUR

Page 18: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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?

Page 19: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen

EXERCISE 3

Find the length of the segment AB, if possible.

Page 20: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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.

Page 21: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

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

Page 22: Grade 8 The Concept of Congruence Module two. TOPIC D The Pythagorean Theorem.

NYS COMMON CORE MATHEMATICS CURRICULUM 8.2Lesson sixteen

Lesson Summary


The Pythagorean Theorem Section 8-1. Use the Pythagorean Theorem.

The Pythagorean Theorem Section 8-1. Use the Pythagorean Theorem.

703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem… · 2020-02-10 · 703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem:

703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem… · 2020-02-10 · 703 Pythagorean Theorem — Day 1 Essential Question: VOCAB Pythagorean Theorem:

4-8 The Pythagorean Theorem 0806.4.1 Use and apply the Pythagorean Theorem to solve contextual problems The Pythagorean Theorem.

4-8 The Pythagorean Theorem 0806.4.1 Use and apply the Pythagorean Theorem to solve contextual problems The Pythagorean Theorem.

The Pythagorean Theorem and Its Converse. Use the Pythagorean Theorem Use the Converse of the Pythagorean Theorem.

The Pythagorean Theorem and Its Converse. Use the Pythagorean Theorem Use the Converse of the Pythagorean Theorem.

9.2 The Pythagorean Theorem Geometry. Objectives/Assignment Prove the Pythagorean Theorem Use the Pythagorean Theorem to solve real-life problems such.

9.2 The Pythagorean Theorem Geometry. Objectives/Assignment Prove the Pythagorean Theorem Use the Pythagorean Theorem to solve real-life problems such.

Pythagorean Theorem .

Pythagorean Theorem .

Demonstration of the Pythagorean Theorem · Pythagorean Theorem Mathematics ... Demonstration of the Pythagorean Theorem ... The"top"portion"of"the"map"shows"the"Pythagorean"Theorem"expressed"in"the"form"a2

Demonstration of the Pythagorean Theorem · Pythagorean Theorem Mathematics ... Demonstration of the Pythagorean Theorem ... The"top"portion"of"the"map"shows"the"Pythagorean"Theorem"expressed"in"the"form"a2

Pythagorean Theorem 5.4. Learn the Pythagorean Theorem. Define Pythagorean triple. Learn the Pythagorean Inequality. Solve problems with the Pythagorean.

Pythagorean Theorem 5.4. Learn the Pythagorean Theorem. Define Pythagorean triple. Learn the Pythagorean Inequality. Solve problems with the Pythagorean.

Pythagorean Theorem Inequality and Pythagorean Triples

Pythagorean Theorem Inequality and Pythagorean Triples

Pythagorean Theorem

Pythagorean Theorem

11.2 Pythagorean Theorem

11.2 Pythagorean Theorem

9.2 The Pythagorean Theorem Did Pythagoras of Samos discover the Pythagorean theorem?

9.2 The Pythagorean Theorem Did Pythagoras of Samos discover the Pythagorean theorem?

Prove pythagorean theorem

Prove pythagorean theorem

The Pythagorean Theorem

The Pythagorean Theorem

Pythagorean Theorem. History of Pythagorean Theorem Review The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569.

Pythagorean Theorem. History of Pythagorean Theorem Review The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569.

8.1 Pythagorean Theorem and Pythagorean Triples

8.1 Pythagorean Theorem and Pythagorean Triples

Pythagorean Theorem 170720 - josmfs.netjosmfs.net/.../2018/12/Pythagorean-Theorem-170720.pdf · Pythagorean Theorem 170720.doc 1 The Pythagorean Theorem 27 March 2016, rev 28 December

Pythagorean Theorem 170720 - josmfs.netjosmfs.net/.../2018/12/Pythagorean-Theorem-170720.pdf · Pythagorean Theorem 170720.doc 1 The Pythagorean Theorem 27 March 2016, rev 28 December

The Pythagorean Theorem

The Pythagorean Theorem

Big and Small - CUSD 4...Proving the Pythagorean Theorem Proving the Pythagorean Theorem and the Converse of the Pythagorean Theorem 1. Use this figure to prove the Pythagorean Theorem.

Big and Small - CUSD 4...Proving the Pythagorean Theorem Proving the Pythagorean Theorem and the Converse of the Pythagorean Theorem 1. Use this figure to prove the Pythagorean Theorem.

Pythagorean Theorem Unit

Pythagorean Theorem Unit