Question

the vertices of $\triangle ghj$ are $g(-2, - 2)$, $h(-2,6)$, and $j(4,6)$. if $\triangle klmcong\triangle ghj$, find $kl$, $lm$, and $km$.
$kl=square$ (type an integer or a decimal.)
$lm=square$ (type an integer or a decimal.)
$km=square$ (type an integer or a decimal.)

Explanation:

Answer:

First, find the side - lengths of \(\triangle GHJ\) using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
The distance between \(G(-2,-2)\) and \(H(-2,6)\):
Since \(x_1=x_2 = - 2\), \(GH=\vert6-( - 2)\vert=8\).
The distance between \(H(-2,6)\) and \(J(4,6)\):
Since \(y_1 = y_2=6\), \(HJ=\vert4-( - 2)\vert=6\).
The distance between \(G(-2,-2)\) and \(J(4,6)\):
\(d=\sqrt{(4-( - 2))^2+(6-( - 2))^2}=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\).
Since \(\triangle KLM\cong\triangle GHJ\), corresponding sides are equal.
(a) \(KL = 8\)
(b) \(LM = 6\)
(c) \(KM = 10\)