Question

question 5 points 2 rectangle lmno ≅ ghil. find the sides of the rectangle ghil. image of two rectangles: lmno with length 13 in and width 15 in, and ghil options: gh = 14 in, hi = 15 in, il = 14 in, and lg = 15 in; gh = 13 in, hi = 15 in, il = 13 in, and lg = 15 in; gh = 15 in, hi = 13 in, il = 13 in, and ol = 15 in; gh = 12 in, hi = 11 in, il = 11 in, and ol = 12 in

Explanation:

Step1: Recall Congruent Figures Property

Congruent rectangles have equal corresponding sides. So, sides of \( LMNO \) and \( GHIL \) should match.

Step2: Identify Sides of \( LMNO \)

From the diagram, \( LM = ON = 13 \) in (length) and \( LO = MN = 15 \) in (width).

Step3: Match Sides to \( GHIL \)

For \( GHIL \), \( GH \) corresponds to \( LM \) (length), \( HI \) corresponds to \( LO \) (width), \( IL \) corresponds to \( MN \) (length), and \( LG \) corresponds to \( LO \) (width)? Wait, no—wait, rectangle \( GHIL \): \( GH \) and \( IL \) are lengths, \( HI \) and \( LG \) are widths. So \( GH = LM = 13 \) in, \( HI = LO = 15 \) in, \( IL = GH = 13 \) in, \( LG = HI = 15 \) in. Checking options, the second option has \( GH = 13 \) in, \( HI = 15 \) in, \( IL = 13 \) in, \( LG = 15 \) in.

Answer:

B. \( GH = 13 \) in, \( HI = 15 \) in, \( IL = 13 \) in, and \( LG = 15 \) in (assuming the second option is labeled as B; if original options had labels, use the correct label with text. Since the options are listed, the correct one is the second option: \( GH = 13 \) in, \( HI = 15 \) in, \( IL = 13 \) in, and \( LG = 15 \) in)