Question

In the diagram at the right, sides SV and RW are parallel. Explain why RTW is similar to STV.​

Answer 1

Similar Triangles must have matching angles, so you need to prove the angles all match.

Explanation:

1.

Angle RTW = Angle STV becasue it's the same angle.

2.

Because ST is parallel to RW and RT cuts through those two parallel lines, you have

Angle TSV = Angle TRW because they are corresponding angles.

3.

Because ST is parallel to RW and TW cuts through those two parallel lines, you have

Angle TVS = Angle TWR because they are corresponding angles.

So now you know the three angles in each triangle match the three angles in the other triangle. They're similar triangles.