Which pair of triangles must be similar?
A. Triangles 1 and 2 each have a 35° angle.
B. Triangles 3 and 4 are both isosceles. They each have a 40° angle.
C. Triangle 5 has a 30° angle and a 90° angle. Triangle 6 has a 30° angle and a
70° angle.
D. Triangle 7 has a 50° angle and a 25° angle. Triangle 8 has a 50° angle and a
105° angle.

According to the triangle similarity theorem the two triangles are similar if the two angles of one triangle are congruent with the two angles of the other triangle.

B.

Isosceles triangles as a special case are similar if they have one angle the same and that is an angle of 40°.

D.

Triangle 7 has angles 50°, 25° and 105°

Triangle 8 has angles 50°, 105° and 25°

So they have all three angles congruent and therefore they are similar.

God is with you!!!

hamzaahmeds hamzaahmeds · Answer 2 · 2021-10-19T13:52:25+02:00

This question involves the concept of similar triangles.

The pair of triangles that are similar are "B and D".

A pair of triangles is termed as similar triangles if the two angles of both the triangles are equal to each other. Hence, we will check this condition for each pair given in the question.

A.

Only one angle is given to be equal for both the triangles, while the other two angles are unknown. Hence, this pair can not be termed as similar.

B.

For an isoceles triangle, two sides and two angles of the triangle are equal. Considering the 40° angle to be the equal angle, we can safely conclude that the two angles of both the triangles in the pair are the same. Hence, this pair can be termed as similar.

C.

Triangle 5 has angles: 30°, 90° and (180°-30°-90°) = 60°. While triangle 6 has angles: 30°, 70°, and (180°-70°-30°) = 80°. Since all the angles of both the triangles are different. Therefore, they can not be termed as similar.

D.

Triangle 7 has angles: 50°, 20° and (180°-50°-25°) = 105°. While triangle 6 has angles: 50°, 105°, and (180°-50°-105°) = 25°. Since all the angles of both the triangles are equal. Therefore, they can be termed as similar.

Learn more about similar triangles here:

https://brainly.com/question/19738610?referrer=searchResults

The attached picture shows the conditions for similar triangles.