Question

1. which triangles are congruent by asa?

a △hgf and △tvu
b △vtu and △hgf
c △vtu and △abc
d none of these

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) congruence criterion

ASA states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze each option

• For option A: $\triangle HGF$ and $\triangle TVU$

Check the angles and included side. There is no information given that two angles and the included side of $\triangle HGF$ are equal to two angles and the included side of $\triangle TVU$.

• For option B: $\triangle VTU$ and $\triangle HGF$

Let's assume in $\triangle VTU$ and $\triangle HGF$:
If we consider the angles and the included side. Suppose the marked angles and the marked side.
In $\triangle VTU$, we have two angles and the included side. In $\triangle HGF$, we can match the two angles (the non - right - angled marked angles) and the included side (the side with two marks) such that by ASA, $\triangle VTU\cong\triangle HGF$.

• For option C: $\triangle VTU$ and $\triangle ABC$

There is no indication that two angles and the included side of $\triangle VTU$ are equal to two angles and the included side of $\triangle ABC$.

Answer:

B. $\triangle VTU$ and $\triangle HGF$