Question

Find the values of K and J that prove the two triangles are congruent using the SSS congruence postulate.

Answer 1

The triangles are congruent by the SSS postulate if:

16/9k-231 = 524/3 (1)

And

K+5/6 = 10j-17 (2)

Let's solve equation (1) first:

$\begin{gathered} \frac{16}{9}k-231=\frac{524}{3} \\ \frac{16}{9}k-\frac{2079}{9}=\frac{1569}{9} \\ 16k-2079=1569 \\ 16k=1569+2079 \\ 16k=3648 \\ k=228 \end{gathered}$

Now, for equation (2)

$\begin{gathered} k+\frac{5}{6}=10j-17 \\ 228+\frac{5}{6}=10j-17 \\ 10j=211+\frac{5}{6} \\ 10j=\frac{1266+5}{6} \\ 60j=1271 \end{gathered}$