Which of these conditions might be true if polygons abcd and klmn are similar?

Asked by maham237 @ in Mathematics viewed by 455 People

Which of these conditions might be true if polygons ABCD and KLMN are similar? 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.
B. 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.
C. The lengths of corresponding sides of ABCD and KLMN are equal, but the measures of corresponding angles of ABCD and KLMN are not equal.
D. The lengths of corresponding sides of ABCD and KLMN are proportional, but the measures of corresponding angles of ABCD and KLMN are not equal.
E.The measures of corresponding angles of ABCD and KLMN are not proportional, but the lengths of corresponding sides of ABCD and KLMN are proportional.

Answered by maham237 @


The correct answer 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.


Explanation:


The definition of similar polygons is two polygons whose corresponding angles are congruent and whose corresponding sides are proportional.


If the lengths of the corresponding sides of ABCD are half of those of KLMN, this is the proportion 1:2.


Combined with the fact that the measures of the corresponding angles are congruent, this makes ABCD and KLMN similar polygons.


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