which of these conditions might be true if polygons abcd and klmn are similar?\na. the measures of…

which of these conditions might be true if polygons abcd and klmn are similar?\na. the measures of corresponding angles of abcd and klmn are equal, but the lengths of corresponding sides of abcd are half those of klmn.\nb. 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.\nc. the lengths of corresponding sides of abcd and klmn are equal, but the measures of corresponding angles of abcd and klmn are not equal.\nd. the lengths of corresponding sides of abcd and klmn are proportional, but the measures of corresponding angles of abcd and klmn are not equal.\ne. the measures of corresponding angles of abcd and klmn are not proportional, but the lengths of corresponding sides of abcd and klmn are proportional.

which of these conditions might be true if polygons abcd and klmn are similar?\na. the measures of corresponding angles of abcd and klmn are equal, but the lengths of corresponding sides of abcd are half those of klmn.\nb. 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.\nc. the lengths of corresponding sides of abcd and klmn are equal, but the measures of corresponding angles of abcd and klmn are not equal.\nd. the lengths of corresponding sides of abcd and klmn are proportional, but the measures of corresponding angles of abcd and klmn are not equal.\ne. 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

Explanation:

Step1: Recall similarity definition

Two polygons are similar if corresponding - angles are equal and corresponding - sides are proportional.

Step2: Analyze option A

If the measures of corresponding angles of (ABCD) and (KLMN) are equal, and the lengths of corresponding sides of (ABCD) are half those of (KLMN), the sides are proportional (with a scale - factor of (\frac{1}{2})). This satisfies the definition of similar polygons.

Step3: Analyze option B

For polygons to be similar, if angles are in a non - 1:1 ratio, they are not equal, and non - proportional sides violate the similarity criteria.

Step4: Analyze option C

Equal sides do not imply similarity if angles are not equal. Similarity requires equal angles and proportional sides.

Step5: Analyze option D

Proportional sides are not enough; corresponding angles must also be equal for polygons to be similar.

Step6: Analyze option E

Non - proportional angles and proportional sides do not meet the requirements for polygon similarity.

Answer:

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).