Geometry 8-1 Complete Lesson: The Pythagorean Theorem and Its Converse
By Matthew Richardson
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Last updated over 3 years ago
25 questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
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Question 1
1.
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.
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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Question 2
2.
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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Question 3
3.
Problem 1 Got It? Do the side lengths in the previous item form a Pythagorean triple? Explain.
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Question 4
4.
Problem 2 Got It?
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Question 5
5.
Problem 3 Got It?
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Question 6
6.
Problem 4 Got It? A triangle has side lengths 16, 48, and 50. Is the triangle a right triangle? Explain.
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Question 7
7.
Problem 5 Got It?
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Question 8
8.
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Question 9
9.
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Question 10
10.
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Question 11
11.
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Question 13
13.
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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Question 14
14.
Review Lesson 7-5: â–³ABC has side lengths AB = 8, BC = 9, and AC = 10.
1. Sketch â–³ABC. 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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Question 15
15.
Preview Lesson 8-2: Simplify the expression.
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Question 16
16.
Preview Lesson 8-2: Simplify the expression.
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Question 17
17.
Preview Lesson 8-2: Simplify the expression.
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Question 18
18.
Enter only a number.
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Question 19
19.
Enter only a number.
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Question 20
20.
Enter only a number.
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Question 21
21.
Enter only a number.
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Question 22
22.
Use Your Vocabulary: The hypotenuse is the longest side in a right triangle.
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Question 23
23.
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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Question 24
24.
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.
The side lengths of the triangle form a Pythagorean triple.
