Question

1. which pair of triangles can be proved congruent by the sas postulate? given: $overline{ca}congoverline{ce}$, $overline{ab}congoverline{de}$ $\triangle abx$ and $\triangle edx$ $\triangle acd$ and $\triangle eda$ $\triangle ade$ and $\triangle eba$

Explanation:

Step1: Recall SAS (Side - Angle - Side) postulate

The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the given congruent sides

We are given $\overline{CA}\cong\overline{CE}$ and $\overline{AB}\cong\overline{DE}$. We need to find the pair of triangles where these sides are part of the two - side and included - angle setup.
In $\triangle ABE$ and $\triangle EDA$, we know that $\overline{AB}\cong\overline{DE}$ (given), $\overline{AE}$ is common to both triangles, and since $\overline{CA}\cong\overline{CE}$, the angles opposite to these equal sides in the larger triangles formed contribute to the included - angle condition.
For $\triangle ABX$ and $\triangle EDX$, we don't have enough information from the given $\overline{CA}\cong\overline{CE}$ and $\overline{AB}\cong\overline{DE}$ to use SAS. For $\triangle ACD$ and $\triangle EDA$, the given side - congruence relationships do not align with the sides of these two triangles for SAS.

Answer:

$\triangle ADE$ and $\triangle EBA$