Assessment: Similarity

Two similar triangles must have:

In a²+b²=c², what is c?

In △ABC, DE ∥ BC. AD=5, DB=10, AE=4. Find EC.

A right triangle has legs 9 and 12. Find the hypotenuse.

In △ABC, AD bisects ∠A. AB=8, AC=12, BC=25. Find DC.

A 30-60-90 triangle has hypotenuse 20. Find the short leg (opposite the 30° angle).

A student and a flagpole cast shadows at the same time. Why does this form similar triangles?

A ladder 13 m long leans against a wall, with its base 5 m from the wall. How high up the wall does it reach?

Why does DE ∥ BC in △ABC guarantee △ADE ~ △ABC?

In △ABC, AD bisects ∠A. AB=10, AC=15, and DC=12. Find BD.