contestada

AB = x + 2
DC = 22 − x
AD = 6 + y
BC = 3y
Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs.
A) 6, 3
B) 9, 6
C) 12, 6
D) 12, 9

Respuesta :

calculista

Answer:

Option D) 12, 9

Step-by-step explanation:

we know that

In a parallelogram opposite side are parallel and congruent

so

In the parallelogram ABCD

opposite sides are

AB and DC

BC and AD

so

AB=CD

BC=AD

step 1

Find the value of x

AB=DC

substitute the values

[tex]x+2=22-x[/tex]

solve for x

[tex]x+x=22-2[/tex]

[tex]2x=20[/tex]

[tex]x=10[/tex]

step 2

Find the value of side AB

[tex]AB=x+2[/tex]

substitute the value of x

[tex]AB=10+2=12\ units[/tex]

step 3

Find the value of y

BC=AD

substitute the values

[tex]3y=6+y[/tex]

solve for y

[tex]3y-y=6[/tex]

[tex]2y=6[/tex]

[tex]y=3[/tex]

step 4

Find the value of BC

[tex]BC=3y[/tex]

substitute the value of y

[tex]BC=3(3)=9\ units[/tex]

therefore

The length of the opposite side pairs are 12 and 9

Answer:

D

Step-by-step explanation:

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