Question

1. how are the following triangle congruent? if they are not congruent then choose nei (not enough information or not possible)

Explanation:

Step1: Analyze first - pair of triangles

We have vertical angles at \(x\). Also, two pairs of corresponding sides are congruent (marked with dashes). By Side - Angle - Side (SAS) congruence criterion (the included angle between the two pairs of congruent sides is equal due to vertical angles), the first pair of triangles \(\triangle VWX\) and \(\triangle YZX\) are congruent.

Step2: Analyze second - pair of triangles

We have right - angles at \(T\) and \(E\), a pair of congruent legs (marked with dashes) and the hypotenuse is common (\(CR\) is common to both \(\triangle CTR\) and \(\triangle CER\)). By Hypotenuse - Leg (HL) congruence criterion for right triangles, the second pair of triangles are congruent. But since HL is not among the given options, and we can also consider Side - Angle - Side as we have a right - angle as the included angle between the common hypotenuse and the congruent leg, so it is also congruent by SAS.

Answer:

For the first pair of triangles: Side - Angle - Side
For the second pair of triangles: Side - Angle - Side