Question

Determine if the triangles, △YPQ and △NPD, are similar. if so, Identify criterion.

Answer 1

Yes, they are similar.

Criterion: AA Similarity

Step-by-step explanation:

Looking at triangles YPQ and NPD, we can see that angles NPD and YPQ are vertically opposite angles and are congruent since vertically opposite angles are always congruent;

`\angle YPQ\cong\angle NPD\text{ (vertically opposite angles)}`

We can also observe that angles N and Y are congruent since they are alternate angles;

`\angle N\cong\angle Y\text{ (alternate angles)}`

From the AA similarity rule, we know that two triangles are said to be similar if two angles in one triangle are equal to two triangles in the other triangle.

Therefore, from the AA rule, we can say that triangles YPQ and NPD are similar.