Quadrilateral ABCDABCDA, B, C, D has the following vertices:

A(6,8)A(6,8)A, left parenthesis, 6, comma, 8, right parenthesis

B(6,-5)B(6,−5)B, left parenthesis, 6, comma, minus, 5, right parenthesis

C(-5,-10)C(−5,−10)C, left parenthesis, minus, 5, comma, minus, 10, right parenthesis

D(-5,3)D(−5,3)D, left parenthesis, minus, 5, comma, 3, right parenthesis

Is quadrilateral ABCDABCDA, B, C, D a rhombus, and why?

Choose 1

Choose 1

(Choice A)

A

Yes, because AB=BC=CD=ADAB=BC=CD=ADA, B, equals, B, C, equals, C, D, equals, A, D.

(Choice B)

B

Yes, because \overline{AB} \parallel \overline{CD}

AB

∥

CD

start overline, A, B, end overline, \parallel, start overline, C, D, end overline, and \overline{BC} \parallel \overline{AD}

BC

∥

AD

start overline, B, C, end overline, \parallel, start overline, A, D, end overline.

(Choice C)

C

No, because \overline{AB}

AB

start overline, A, B, end overline is longer than \overline{BC}

BC

start overline, B, C, end overline.

(Choice D)

D

No, because \overline{AB}

AB

start overline, A, B, end overline is not parallel to \overline{BC}

BC

start overline, B, C, end overline.