Question

How do I get to the answer of this question?

Answer 1

Since the quadrilateral FISH is originated from quadrilateral BEAR after a reflection and a dilation, therefore the quadrilaterals are similar.

Since they are similar, the corresponding angles are congruent, therefore angles A and S are congruent (statement I is true).

Also, the corresponding sides are proportional, so we can write the following proportion:

$\frac{BE}{FI}=\frac{AR}{SH}$

Therefore statement II is also true.

Since quadrilateral BEAR had a dilation with a scale factor of 3 to generate quadrilateral FISH, so the second quadrilateral has a perimeter 3 times the perimeter of the first quadrilateral. Therefore statement III is false, the perimeters are not congruent.

The true statements are I and II only, therefore the correct option is c.