Question

determining unknown measures of congruent figures. given △xyz ≅ △egf, find the measurements of the unknown sides and angles. zx = in. eg = in. m∠x = °. m∠g = °.

Explanation:

Step1: Recall congruent - triangle property

Corresponding sides of congruent triangles are equal. So, if $\triangle XYZ\cong\triangle EGF$, then $ZX = EF$.
$ZX=1.3$ in.

Step2: Find the length of $EG$

Corresponding sides of congruent triangles are equal. So, $EG = YZ$.
$EG = 3.0$ in.

Step3: Find the measure of $\angle X$

Corresponding angles of congruent triangles are equal. So, $m\angle X=m\angle E$.
$m\angle X = 48^{\circ}$

Step4: Find the measure of $\angle G$

First, find the measure of $\angle Y$ in $\triangle XYZ$. Using the angle - sum property of a triangle ($m\angle X + m\angle Y+m\angle Z=180^{\circ}$), we have $m\angle Y=180^{\circ}-(107^{\circ} + 48^{\circ})=25^{\circ}$. Since corresponding angles of congruent triangles are equal, $m\angle G=m\angle Y$.
$m\angle G = 25^{\circ}$

Answer:

$ZX = 1.3$ in.
$EG = 3.0$ in.
$m\angle X = 48^{\circ}$
$m\angle G = 25^{\circ}$