Question

1. dig deeper! the houses are identical. a. what is the length of side lm? b. which angle of jklmn corresponds to ∠d? c. side ab is congruent to side ae. what is the length of side ab? what is the perimeter of abcde?

Explanation:

Step1: Use congruence of houses

Since the houses are identical, corresponding sides are equal. Side $LM$ corresponds to side $BC$. So $LM = 32$ ft.

Step2: Identify corresponding angles

Corresponding angles of congruent - shaped figures are equal. $\angle D$ corresponds to $\angle N$.

Step3: Find side length and perimeter

Given $AB\cong AE$ and $AE = 12$ ft, so $AB = 12$ ft. The perimeter of $ABCDE$ is $AB + BC+CD + DE+EA=12 + 32+12 + 12+12=80$ ft.

Answer:

a. 32 ft
b. $\angle N$
c. $AB = 12$ ft, perimeter of $ABCDE = 80$ ft