An illustration shows two quadrilaterals, one big and one small. The smaller quadrilateral is A B C D and the bigger one is H G F E.Which statement represents the similarity between the two figures?

Answer 1

To establish the similarity between the two quadrilaterals ABCD (the smaller one) and HGFEn (the larger one), you can look for the following characteristics:

1. Corresponding Angles: If the corresponding angles of quadrilateral ABCD and quadrilateral HGFEn are equal (i.e., ∠A = ∠H, ∠B = ∠G, ∠C = ∠F, ∠D = ∠E), then the quadrilaterals are similar.

2. Proportional Sides: If the lengths of the corresponding sides of the two quadrilaterals are in proportion (i.e., AB/HG = BC/GF = CD/FE = DA/EH), then they are similar.

The statement that best represents the similarity between quadrilateral ABCD and quadrilateral HGFEn can be summarized as:

"Quadrilateral ABCD is similar to quadrilateral HGFEn (ABCD ~ HGFEn) because their corresponding angles are equal and the lengths of their corresponding sides are proportional."

This captures both the angle and side length criteria necessary for establishing similarity between the two shapes.