Question

Which pair of triangles must be similar?

Group of answer choices
a. Triangles 1 and 2 each have a 350 angle.
b. Triangles 3 and 4 are both isosceles. They each have a 400 angle.
c. Triangle 5 has a 300 angle and a 900 angle. Triangle 6 has a 300 angle and a 700 angle.
d. Triangle 7 has a 500 angle and a 250 angle. Triangle 8 has a 500 angle and a 1050 angle.

Answer 1

In order for triangles to be similar, their corresponding angles must be congruent. Triangles 1 and 2 are similar because they each have a 350 angle.

Step-by-step explanation:

In order for two triangles to be similar, their corresponding angles must be congruent.

From the given options:

a. Triangles 1 and 2 each have a 350 angle. Since the angles are congruent, these two triangles are similar.

b. Triangles 3 and 4 are both isosceles and each have a 400 angle. Although the angles are congruent, we cannot determine if the triangles are similar based on this information alone.

c. Triangle 5 has a 300 angle and a 900 angle. Triangle 6 has a 300 angle and a 700 angle. The angles are not congruent, so these triangles are not similar.

d. Triangle 7 has a 500 angle and a 250 angle. Triangle 8 has a 500 angle and a 1050 angle. The angles are not congruent, so these triangles are not similar.

Therefore, the pair of triangles that must be similar is triangles 1 and 2 (option a).