Answer:
Quadrilateral ABCD is a parallelogram when value of x is 4 and y is 4.
Step-by-step explanation:
Given:
Length of AB = [tex]4x[/tex]
Length of DC = 16
Length of AD = [tex]y+4[/tex]
Length of BC = [tex]2y[/tex]
Also Given:
In quadrilateral ABCD, we can say opposite sides are AB and DC and other Opposite sides are BC and AD.
hence we can check both for both equality
Length AB = Length of DC
Substituting the values we get;
[tex]4x=16\\\\x=\frac{16}{4}=4[/tex]
when x=4
Length of AB = [tex]4x=4\times4 =16[/tex] which is equal to Length of DC
Also for other pair;
Length BC = Length of AD
Substituting the values we get;
[tex]y+4=2y\\\\2y-y = 4\\\\y= 4[/tex]
Hence Length of AD = [tex]y+4= 4+4 =8[/tex]
Length of BC = [tex]2y = 2\times 4 =8[/tex]
Hence Length of AD = Length of BC
Since both pairs of opposite sides are congruent.
Hence, Quadrilateral ABCD is a parallelogram when value of x is 4 and y is 4.
