Question

Which of these conditions might be true if polygons ABCD and KLMN are similar? The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN. The measures of corresponding angles of ABCD and KLMN are in the ratio 1 : 2, but the lengths of corresponding sides of ABCD and KLMN are not proportional. The lengths of corresponding sides of ABCD and KLMN are equal, but the measures of corresponding angles of ABCD and KLMN are not equal. The lengths of corresponding sides of ABCD and KLMN are proportional, but the measures of corresponding angles of ABCD and KLMN are not equal. The measures of corresponding angles of ABCD and KLMN are not proportional, but the lengths of corresponding sides of ABCD and KLMN are proportional.

Answer 1

The question ask to choose among the following choices that state the truth about the condition if polygon ABCD and KLMN are similar and the answer would be A. The measure of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.

Answer 2

Answer:  The correct option is

(A) The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.

Step-by-step explanation: We are given to select the correct condition that might be true if polygons ABCD and KLMN are similar.

Two polygons are said to be SIMILAR if corresponding angles are congruent and corresponding sides are proportional.

So, options (B), (C), (D) and (E) are not correct because they contradict conditions of similarity.

In option (A), we have

The measures of corresponding angles of ABCD and KLMN are equal. So, they must be congruent.

And the lengths of corresponding sides of ABCD are half those of KLMN.

So, we can write

$AB=\dfrac{1}{2}KL,~~BC=\dfrac{1}{2}LM,~~CD=\dfrac{1}{2}MN,~~AD=\dfrac{1}{2}KN\\\\\\\Rightarrow \dfrac{AB}{KL}=\dfrac{BC}{LM}=\dfrac{CD}{MN}=\dfrac{AD}{KN}=\dfrac{1}{2}.$

Therefore, the corresponding sides are proportional.

Thus, option (A) is true if two polygons are similar.