Question

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 $DF = JL$.
We have the equation $9x - 23=7x - 11$.

Step2: Solve the equation for $x$

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

Step3: Use another congruent - side property

Also, $DE = JK$. But we are not given any information about $y$ from the side - length equalities we've used so far. Since $DE = 18$ and $JK = 3y-21$, we set up the equation $3y-21 = 18$.

Step4: Solve the equation for $y$

Add 21 to both sides: $3y-21 + 21=18 + 21$.
$3y=39$.
Divide both sides by 3: $\frac{3y}{3}=\frac{39}{3}$, so $y = 13$.

Answer:

$x = 6,y = 13$