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.
2 answers:
The task is to select from the provided options that accurately represent the conditions under which polygons ABCD and KLMN would be considered similar; hence the selected answer is A. The angles of ABCD and KLMN that correspond are equal, while the side lengths of ABCD are half those of KLMN.
Answer: The correct choice is
(A) The angles of ABCD and KLMN corresponding to each other are equal, but the sides of ABCD are half the length of those in KLMN.
Step-by-step explanation: It is required to identify which statement reflects the potential truth if the polygons ABCD and KLMN are similar.
Two polygons are considered SIMILAR when their corresponding angles are congruent and the sides are in proportion.
Hence, options (B), (C), (D), and (E) are incorrect since they contradict the principles of similarity.
In option (A), we see
The angles of ABCD and KLMN that correspond are equal. Thus, they must be congruent.
Moreover, the lengths of corresponding sides of ABCD are half those of KLMN.
Thus, we can deduce
Consequently, the corresponding sides are proportional.
Therefore, option (A) holds true if the two polygons are similar.
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