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For parallelogram ABCD, find the value of x. A 3x + 20 5 – 12

For parallelogram ABCD, find the value of x. A 3x + 20 5 – 12

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Question 1 (1 point) **For parallelogram ABCD, find the value of x.** The diagram shows a parallelogram labeled as follows: - The vertices are A, B, C, and D. - The top side \( \overline{BC} \) is labeled \( 3x + 20 \). - The bottom side \( \overline{AD} \) is labeled \( 5x - 12 \). #### Options: - a) 10.25 - b) 16 - c) 32 - d) 4 **Explanation:** To determine the value of \( x \), utilize the property of parallelograms that states opposite sides are equal in length. Therefore, \[ 3x + 20 = 5x - 12 \] Solving this equation for \( x \) will provide the answer.
Transcribed Image Text:### Question 1 (1 point) **For parallelogram ABCD, find the value of x.** The diagram shows a parallelogram labeled as follows: - The vertices are A, B, C, and D. - The top side \( \overline{BC} \) is labeled \( 3x + 20 \). - The bottom side \( \overline{AD} \) is labeled \( 5x - 12 \). #### Options: - a) 10.25 - b) 16 - c) 32 - d) 4 **Explanation:** To determine the value of \( x \), utilize the property of parallelograms that states opposite sides are equal in length. Therefore, \[ 3x + 20 = 5x - 12 \] Solving this equation for \( x \) will provide the answer.
**ABCD** is an isosceles trapezoid with vertices **A(10, -1)**, **B(8, 3)**, and **C(-1, 3)**. Find the coordinates of vertex **D**. - **a.** \( D(-3, -1) \) - **b.** \( D(-10, -11) \) - **c.** \( D(-1, 8) \) - **d.** \( D(-1, -3) \) This problem presents an isosceles trapezoid where three vertices are given and asks for the coordinates of the fourth vertex. An isosceles trapezoid has one pair of non-parallel sides (legs) that are congruent.
Transcribed Image Text:**ABCD** is an isosceles trapezoid with vertices **A(10, -1)**, **B(8, 3)**, and **C(-1, 3)**. Find the coordinates of vertex **D**. - **a.** \( D(-3, -1) \) - **b.** \( D(-10, -11) \) - **c.** \( D(-1, 8) \) - **d.** \( D(-1, -3) \) This problem presents an isosceles trapezoid where three vertices are given and asks for the coordinates of the fourth vertex. An isosceles trapezoid has one pair of non-parallel sides (legs) that are congruent.
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