Question

question 5 (multiple choice worth 2 points) (congruence and similarity mc) two rectangles are given. which statement accurately describes the relationship between the given rectangles? lmno ~ xyzw lmno ≅ xyzw lmno ~ wxyz lmno ≅ wxyz

Explanation:

Step1: Recall similarity and congruence rules

For two rectangles to be congruent, all corresponding sides must be equal. For similarity, the ratios of corresponding sides must be equal.

Step2: Calculate side - length ratios

In rectangle LMNO, sides are 6 and 12. In rectangle XYZW, sides are 6 and 3. The ratio of the longer sides of the two rectangles is $\frac{12}{3}=4$, and the ratio of the shorter sides is $\frac{6}{6} = 1$. Since the ratios of corresponding sides are not all equal, the rectangles are not congruent.

Step3: Check for similarity with correct vertex - pairing

If we pair the rectangles as LMNO and XYZW, the ratio of the longer side of LMNO to the longer side of XYZW is $\frac{12}{3}=4$ and the ratio of the shorter side of LMNO to the shorter side of XYZW is $\frac{6}{6}=1$. But if we consider the similarity notation, we need to match the corresponding angles. For similar rectangles, the correct similarity statement is LMNO ~ XYZW as the angles of rectangles are all right - angles (equal) and we match the sides in proportion.

Answer:

A. LMNO ~ XYZW