Question

what additional information do you need to prove $\triangle abc cong \triangle xyz$ by sas
$\bigcirc ac cong zy$
$\bigcirc bc cong yz$
$\bigcirc angle a cong angle x$
$\bigcirc angle b cong angle y$

Explanation:

Step1: Recall SAS congruence rule

SAS (Side-Angle-Side) requires two pairs of congruent sides, with the included angle between them being congruent.

Step2: Identify given congruent sides

From the diagram: $AB \cong XY$, $AC \cong XZ$.

Step3: Find the included angles

For $\triangle ABC$, the angle between $AB$ and $AC$ is $\angle A$. For $\triangle XYZ$, the angle between $XY$ and $XZ$ is $\angle X$.

Step4: Match required congruence

To satisfy SAS, we need the included angles to be congruent: $\angle A \cong \angle X$.

Answer:

$\boldsymbol{\angle A \cong \angle X}$