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-4 A -3 -2 B 7 6 3 2 -10 -1- -2 2 D 3 4 C 5 6 Given the points A(-3,5), B(-1, 1), C(5, 1) and D(3,5), which of the following statements is not a justification that quadrilateral ABCD is a parallelogram? O AD = BC = 6 and AB || DC because they both have a slope of -2. O The diagonals AC and BD share a midpoint at (1,3). O Both pairs of opposite sides are congruent; AB = DC = 2√5 and BC = AD = 6. O Both pairs of opposite sides are parallel since they have the same slope; mAB = mpc = -2 and mAD = mBC = 0

-4 A -3 -2 B 7 6 3 2 -10 -1- -2 2 D 3 4 C 5 6 Given the points A(-3,5), B(-1, 1), C(5, 1) and D(3,5), which of the following statements is not a justification that quadrilateral ABCD is a parallelogram? O AD = BC = 6 and AB || DC because they both have a slope of -2. O The diagonals AC and BD share a midpoint at (1,3). O Both pairs of opposite sides are congruent; AB = DC = 2√5 and BC = AD = 6. O Both pairs of opposite sides are parallel since they have the same slope; mAB = mpc = -2 and mAD = mBC = 0

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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### Justification for Parallelogram AB​CD​ #### Problem Statement: Given the points \( A(-3,5) \), \( B(-1,1) \), \( C(5,1) \), and \( D(3,5) \), which of the following statements is **not** a justification that quadrilateral \(ABCD\) is a parallelogram? ##### Options: 1. \( AD = BC = 6 \) and \( \overline{AB} \parallel \overline{DC} \) because they both have a slope of \( -2 \). 2. The diagonals \( \overline{AC} \) and \( \overline{BD} \) share a midpoint at \( (1,3) \). 3. **(Highlighted Option)** Both pairs of opposite sides are congruent; \( AB = DC = 2\sqrt{5} \) and \( BC = AD = 6 \). 4. Both pairs of opposite sides are parallel since they have the same slope; \( m_{AB} = m_{DC} = -2 \) and \( m_{AD} = m_{BC} = 0 \). #### Explanation of the Graph: The graph is a coordinate plane with a grid. Points \( A \) at \( (-3,5) \), \( B \) at \( (-1,1) \), \( C \) at \( (5,1) \), and \( D \) at \( (3,5) \) are plotted and connected to form quadrilateral \( ABCD \). The graph shows the slopes and lengths of the sides between these points, illustrating the properties used in the justification options. The quadrilateral is drawn to demonstrate whether it satisfies the criteria for being a parallelogram based on the given points.
Transcribed Image Text:### Justification for Parallelogram AB​CD​ #### Problem Statement: Given the points \( A(-3,5) \), \( B(-1,1) \), \( C(5,1) \), and \( D(3,5) \), which of the following statements is **not** a justification that quadrilateral \(ABCD\) is a parallelogram? ##### Options: 1. \( AD = BC = 6 \) and \( \overline{AB} \parallel \overline{DC} \) because they both have a slope of \( -2 \). 2. The diagonals \( \overline{AC} \) and \( \overline{BD} \) share a midpoint at \( (1,3) \). 3. **(Highlighted Option)** Both pairs of opposite sides are congruent; \( AB = DC = 2\sqrt{5} \) and \( BC = AD = 6 \). 4. Both pairs of opposite sides are parallel since they have the same slope; \( m_{AB} = m_{DC} = -2 \) and \( m_{AD} = m_{BC} = 0 \). #### Explanation of the Graph: The graph is a coordinate plane with a grid. Points \( A \) at \( (-3,5) \), \( B \) at \( (-1,1) \), \( C \) at \( (5,1) \), and \( D \) at \( (3,5) \) are plotted and connected to form quadrilateral \( ABCD \). The graph shows the slopes and lengths of the sides between these points, illustrating the properties used in the justification options. The quadrilateral is drawn to demonstrate whether it satisfies the criteria for being a parallelogram based on the given points.
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