Question

Are the following triangles similar? Justify your answer.

Answer 1

Answer:

Yes they are similar.

There are three similarity criteria for triangles.

The first one (AAA) , your case, says that two triangles are similar if their corresponding angles are equal.

The second one (SAS) says that two triangles are similar if two sides have lengths in the same ratio and the angles that are included in these two sides are equal.

The third one (SSS) says that two triangles are similar of all of their sides have lengths in the same ratio.

About the first criteria, you actually need only two corresponding angles to be the same, because the third will always be the difference between 180° and the two angles.

Remember that you CANNOT exceed 180° for the sum of the three angles of a triangle.

And remember also that similarity involves correspondence in sides and angles. Two triangles, with same angles, but mirrored, are not similar!