CPM Homework Help : CCG Problem 7-59

Which pairs of triangles below are congruent and/or similar? For each part, explain how you know using an appropriate triangle congruence or similarity condition. Note: The diagrams are not necessarily drawn to scale.

Hint (all):

What does it mean for two triangles to be congruent? What does it mean for two triangles to be similar?
How are these two definitions different?

Hint (a):
Divide each side of the triangle on the left by $3$ .
What do you notice?

Answer (b):
congruent ( $\text{ASA}≅$ or $\text{AAS}≅$ )

Hint (c):
Use the Pythagorean Theorem to solve for the missing side.

Hint (d):
Where is the $12$ located on each triangle?
Answer (d):
similar ( $AA^{\sim}$ ) but not congruent since the two sides of length $12$ are not corresponding