Question

Determine whether quadrilateral ABCD is similar to quadrilateral EFGH. If so, give the similarity statement. answers: A) The quadrilaterals are not similar. B) Impossible to determine. C) ABCD ∼ FEHG D) ABCD ∼ EFGH

Answer 1

Answer: D) ABCD ∼ EFGH

Step-by-step explanation:

From the given picture,

In parallelogram ABCD, ∠A= 80° .

In parallelogram EFGH, ∠E= 100° .

Since the sum of two adjacent angles in a parallelogram is 180°.

So, ∠A + ∠B = 180°

⇒ ∠B = 180° -∠A =  180°- 80° = 100°

So,  ∠B  = 100°

Similarly in parallelogram EFGH, ∠ E= 80° .

Also, the opposite angles of a parallelogram are equal,

∠A =∠C= 80°  and ∠B=∠D=100°

∠E =∠G= 80°  and ∠F=∠H=100°

So, the corresponding angles of both parallelograms are equal.

That means they are similar.

So the required similarity statement : ABCD ∼ EFGH

Hence, the correct option is D.