Given: Quadrilateral EFGH has vertices at E(2, 3), F(-2,5), G(-3, 3), and H(1,1). Prove Quadrilateral EFGH is a parallelogram. 8 6 -8 -6 -4 -20 2 4 6 8 -2 -4 -6 -8 © 2016 StrongMind. Created using GeoGebra. Examine the proof and answer the question. Statements Reasons 1. Quadrilateral EFGH has vertices at E(2, 3), F(-2, 5), G(-3, 3), and H(1, 1). 1. Given 2. The slope of EF 2. Slope formula %3D 1–3 The slope of GH 1-(-3) The slope of FG = = 2. 35 The slope of EH = H 2. 3. EF || GH 3. ? FG || EH 4. Quadrilateral EFGH is a parallelogram. 4. Both pairs of opposite sides of a parallelogram are parallel. Which reason justifies statement 3? O Lines with equal slopes are parallel. O Lines with opposite reciprocal slopes are parallel. O Opposite sides of quadrilaterals are parallel. O ZE, ZF, ZG, and ZH are right angles.
Given: Quadrilateral EFGH has vertices at E(2, 3), F(-2,5), G(-3, 3), and H(1,1). Prove Quadrilateral EFGH is a parallelogram. 8 6 -8 -6 -4 -20 2 4 6 8 -2 -4 -6 -8 © 2016 StrongMind. Created using GeoGebra. Examine the proof and answer the question. Statements Reasons 1. Quadrilateral EFGH has vertices at E(2, 3), F(-2, 5), G(-3, 3), and H(1, 1). 1. Given 2. The slope of EF 2. Slope formula %3D 1–3 The slope of GH 1-(-3) The slope of FG = = 2. 35 The slope of EH = H 2. 3. EF || GH 3. ? FG || EH 4. Quadrilateral EFGH is a parallelogram. 4. Both pairs of opposite sides of a parallelogram are parallel. Which reason justifies statement 3? O Lines with equal slopes are parallel. O Lines with opposite reciprocal slopes are parallel. O Opposite sides of quadrilaterals are parallel. O ZE, ZF, ZG, and ZH are right angles.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 74E
Related questions
Question
![Given:
Quadrilateral EFGH has vertices at E(2, 3), F(-2,5), G(-3,3), and H(1, 1).
Prove:
Quadrilateral EFGH is a parallelogram.
8
6
F
4
-8
9-
-4
-20
4
6
8
-2
-4
-6
-8
© 2016 StrongMind. Created using GeoGebra.
Examine the proof and answer the question.
Statements
Reasons
1. Quadrilateral EFGH has vertices at E(2, 3), F(-2, 5), G(-3,3), and H(1, 1).
1. Given
2. The slope of EF =
-2-2
5 3
2. Slope formula
The slope of GH =3)
1-3
%3D
1-(-3)
The slope of FG = ,
= 2.
3 (-2)
3-5
The slope of EH =B = 2.
1-3
%3D
1-2
3. ?
3. EF || GH
FG || EH
4. Quadrilateral EFGH is a parallelogram.
4. Both pairs of opposite sides of a parallelogram are parallel.
Which reason justifies statement 3?
O Lines with equal slopes are parallel.
O Lines with opposite reciprocal slopes are parallel.
O Opposite sides of quadrilaterals are parallel.
O ZE, ZF, ZG, and ZH are right angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f2ab5f1-0d3c-425f-bc10-ec4282dce5ef%2F43676e43-32fe-42d2-a08d-afeab5700718%2Fwtescla_processed.png&w=3840&q=75)
Transcribed Image Text:Given:
Quadrilateral EFGH has vertices at E(2, 3), F(-2,5), G(-3,3), and H(1, 1).
Prove:
Quadrilateral EFGH is a parallelogram.
8
6
F
4
-8
9-
-4
-20
4
6
8
-2
-4
-6
-8
© 2016 StrongMind. Created using GeoGebra.
Examine the proof and answer the question.
Statements
Reasons
1. Quadrilateral EFGH has vertices at E(2, 3), F(-2, 5), G(-3,3), and H(1, 1).
1. Given
2. The slope of EF =
-2-2
5 3
2. Slope formula
The slope of GH =3)
1-3
%3D
1-(-3)
The slope of FG = ,
= 2.
3 (-2)
3-5
The slope of EH =B = 2.
1-3
%3D
1-2
3. ?
3. EF || GH
FG || EH
4. Quadrilateral EFGH is a parallelogram.
4. Both pairs of opposite sides of a parallelogram are parallel.
Which reason justifies statement 3?
O Lines with equal slopes are parallel.
O Lines with opposite reciprocal slopes are parallel.
O Opposite sides of quadrilaterals are parallel.
O ZE, ZF, ZG, and ZH are right angles.
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