Geometry 8-1 Complete Lesson: The Pythagorean Theorem and Its Converse

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Solve It! The squares below fit into groups of three to satisfy the following equation:

area of square 1 + area of square 2 = area of square 3

Write one of these equations.

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A Pythagorean triple is a set of nonzero whole numbers a, b, and c that satisfy the equation below. 
Some common Pythagorean triples include:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

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Problem 1 Got It? The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse? Enter only a number.

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Problem 1 Got It? Do the side lengths in the previous item form a Pythagorean triple? Explain.

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Problem 2 Got It?

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Problem 3 Got It?

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Problem 4 Got It? A triangle has side lengths 16, 48, and 50. Is the triangle a right triangle? Explain.

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Problem 5 Got It?

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Error Analysis: A triangle has side lengths 16, 34, and 30. Your friend says it is not a right triangle. Look at your friend's work and describe the error.

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Review Lesson 7-5: △ABC has side lengths AB = 8, BC = 9, and AC = 10.
1. Sketch △ABC. Label the vertices and side lengths.
2. Sketch the bisector of ∠A.
3. Find and label the lengths of the segments formed on segment BC by the bisector of ∠A.

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Preview Lesson 8-2: Simplify the expression.

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Preview Lesson 8-2: Simplify the expression.

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Preview Lesson 8-2: Simplify the expression.

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Enter only a number.

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Enter only a number.

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Use Your Vocabulary: The hypotenuse is the longest side in a right triangle.

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Use Your Vocabulary: Classify each statement as True or False.

True
False

The hypotenuse is the longest side in a right triangle.
The hypotenuse of a right triangle can be any one of the three sides.
In a triangle with side lengths 3, 4, and 5, one of the legs measures 4.

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Use Your Vocabulary: Classify each statement as True or False.

True
False

One leg of the triangle has length 9 cm.
The hypotenuse of the triangle has length 12 cm.

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Reflection: Math Success

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Geometry 8-1 Complete Lesson: The Pythagorean Theorem and Its Converse

Solve It! The squares below fit into groups of three to satisfy the following equation:area of square 1 + area of square 2 = area of square 3Write one of these equations.

Problem 1 Got It? The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse? Enter only a number.

Problem 1 Got It? Do the side lengths in the previous item form a Pythagorean triple? Explain.

Problem 2 Got It?

Problem 3 Got It?

Problem 4 Got It? A triangle has side lengths 16, 48, and 50. Is the triangle a right triangle? Explain.

Problem 5 Got It?

Error Analysis: A triangle has side lengths 16, 34, and 30. Your friend says it is not a right triangle. Look at your friend's work and describe the error.

Review Lesson 7-5: △ABC has side lengths AB = 8, BC = 9, and AC = 10. 1. Sketch △ABC. Label the vertices and side lengths. 2. Sketch the bisector of ∠A.3. Find and label the lengths of the segments formed on segment BC by the bisector of ∠A.

Preview Lesson 8-2: Simplify the expression.

Preview Lesson 8-2: Simplify the expression.

Preview Lesson 8-2: Simplify the expression.

Enter only a number.

Enter only a number.

Use Your Vocabulary: The hypotenuse is the longest side in a right triangle.

Use Your Vocabulary: Classify each statement as True or False.

Use Your Vocabulary: Classify each statement as True or False.

Reflection: Math Success

Solve It! The squares below fit into groups of three to satisfy the following equation:area of square 1 + area of square 2 = area of square 3Write one of these equations.

Problem 1 Got It? The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse? Enter only a number.

Problem 1 Got It? Do the side lengths in the previous item form a Pythagorean triple? Explain.

Problem 2 Got It?

Problem 3 Got It?

Problem 4 Got It? A triangle has side lengths 16, 48, and 50. Is the triangle a right triangle? Explain.

Problem 5 Got It?

Error Analysis: A triangle has side lengths 16, 34, and 30. Your friend says it is not a right triangle. Look at your friend's work and describe the error.

Review Lesson 7-5: △ABC has side lengths AB = 8, BC = 9, and AC = 10. 1. Sketch △ABC. Label the vertices and side lengths. 2. Sketch the bisector of ∠A.3. Find and label the lengths of the segments formed on segment BC by the bisector of ∠A.

Preview Lesson 8-2: Simplify the expression.

Preview Lesson 8-2: Simplify the expression.

Preview Lesson 8-2: Simplify the expression.

Enter only a number.

Enter only a number.

Enter only a number.

Enter only a number.

Use Your Vocabulary: The hypotenuse is the longest side in a right triangle.

Use Your Vocabulary: Classify each statement as True or False.

Use Your Vocabulary: Classify each statement as True or False.

Reflection: Math Success

Enter only a number.

Solve It! The squares below fit into groups of three to satisfy the following equation:

area of square 1 + area of square 2 = area of square 3

Write one of these equations.

Review Lesson 7-5: △ABC has side lengths AB = 8, BC = 9, and AC = 10.
1. Sketch △ABC. Label the vertices and side lengths.
2. Sketch the bisector of ∠A.
3. Find and label the lengths of the segments formed on segment BC by the bisector of ∠A.

Solve It! The squares below fit into groups of three to satisfy the following equation:

area of square 1 + area of square 2 = area of square 3

Write one of these equations.

Review Lesson 7-5: △ABC has side lengths AB = 8, BC = 9, and AC = 10.
1. Sketch △ABC. Label the vertices and side lengths.
2. Sketch the bisector of ∠A.
3. Find and label the lengths of the segments formed on segment BC by the bisector of ∠A.