Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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### Geometry Question: Solving for Variables in a Parallelogram #### Problem Statement: **22. Find the value of each variable in the parallelogram.** The given parallelogram is labeled with side lengths and variables: - One side is labeled \( p \) - The opposite side is labeled \( 6 \) - An adjacent side is labeled \( 5 \) - The opposite adjacent side is labeled \( q - 3 \) #### Diagram: A parallelogram with the sides and variables marked as follows: - The left side is labeled \( p \) - The top side is labeled \( 6 \) - The right side is labeled \( 5 \) - The bottom side is labeled \( q - 3 \) #### Possible Answers: 1. \( p = 5 \) and \( q = 6 \) 2. \( p = 6 \) and \( q = 5 \) 3. \( p = 5 \) and \( q = 9 \) 4. \( p = 9 \) and \( q = 5 \) #### Solution Strategy: In a parallelogram, opposite sides are equal in length. Therefore: - \( p \) is equal to the opposite side labeled \( 5 \) - \( q - 3 \) is equal to the opposite side labeled \( 6 \) Set up the equations based on these relationships: 1. \( p = 5 \) 2. \( q - 3 = 6 \) Solve for \( q \): \[ q - 3 = 6 \] \[ q = 6 + 3 \] \[ q = 9 \] Thus, the correct answer is: - \( p = 5 \) - \( q = 9 \) Therefore, the third answer choice is correct: \[ p = 5 \text{ and } q = 9 \]
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Transcribed Image Text:### Geometry Question: Solving for Variables in a Parallelogram #### Problem Statement: **22. Find the value of each variable in the parallelogram.** The given parallelogram is labeled with side lengths and variables: - One side is labeled \( p \) - The opposite side is labeled \( 6 \) - An adjacent side is labeled \( 5 \) - The opposite adjacent side is labeled \( q - 3 \) #### Diagram: A parallelogram with the sides and variables marked as follows: - The left side is labeled \( p \) - The top side is labeled \( 6 \) - The right side is labeled \( 5 \) - The bottom side is labeled \( q - 3 \) #### Possible Answers: 1. \( p = 5 \) and \( q = 6 \) 2. \( p = 6 \) and \( q = 5 \) 3. \( p = 5 \) and \( q = 9 \) 4. \( p = 9 \) and \( q = 5 \) #### Solution Strategy: In a parallelogram, opposite sides are equal in length. Therefore: - \( p \) is equal to the opposite side labeled \( 5 \) - \( q - 3 \) is equal to the opposite side labeled \( 6 \) Set up the equations based on these relationships: 1. \( p = 5 \) 2. \( q - 3 = 6 \) Solve for \( q \): \[ q - 3 = 6 \] \[ q = 6 + 3 \] \[ q = 9 \] Thus, the correct answer is: - \( p = 5 \) - \( q = 9 \) Therefore, the third answer choice is correct: \[ p = 5 \text{ and } q = 9 \]
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