Question

Which pair of triangles MUST be similar?

a.) Triangles 1 and 2 they each have a 40 degree angle.
b.) Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.
c.) Triangle 5 has a 25 degree angle and a 75 degree angle. Triangle 6 has a 25 degree angle and a 70 degree angle.

Answer 1

b.) Triangles 7 and 8 are similar.

Explanation:

If triangles have the same angle measurements, they are similar

If we have two angles, we can find the third by using the equation 180 (total of all angles in any triangle) - angle 1 -angle 2 = angle 3.

Let's set up this value with values from triangle 7.

180-40-35=angle 3

105=angle 3

Thus, the angle measurements of triangle 7 are 35, 40, anf 105.

Let's set up the same equation with value for triangle 8.

180-40-105=angle 3

35=angle 3

Thus, the angle measurements of triangle 8 are 35, 40, anf 105, the same as those of triangle 7, meaning the two triangles are similar.

Answer 2

b.) Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.

Explanation:

b.) triangle 7's 3 angles: 40° , 35° and 180° - 40° - 35° = 105°

triangle 8: 40° , 105° and 180° - 40° - 105° = 35°

they have all 3 corresponding angles congruent, triangle and triangle 8 is similar (AAA)