Question

8 if △def≅△jkl, de = 18, ef = 23, df = 9x - 23, jl = 7x - 11, and jk = 3y - 21, find the values of x and y.

Explanation:

Step1: Use congruent - side property

Since $\triangle DEF\cong\triangle JKL$, corresponding sides are equal. So $DF = JL$.
$9x - 23=7x - 11$

Step2: Solve for x

Subtract $7x$ from both sides:
$9x-7x - 23=7x - 7x-11$
$2x-23=-11$
Add 23 to both sides:
$2x-23 + 23=-11 + 23$
$2x = 12$
Divide both sides by 2:
$x=\frac{12}{2}=6$

Step3: Use another congruent - side property

Also, $EF = JK$. So $23=3y - 21$

Step4: Solve for y

Add 21 to both sides:
$23 + 21=3y-21 + 21$
$44 = 3y$
Divide both sides by 3:
$y=\frac{44}{3}$

Answer:

$x = 6,y=\frac{44}{3}$