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.

D) Triangle 7 has a 50° angle and a 25° angle. Triangle 8 has a 50° angle and a  105° angle

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

Verify each case

case A) Triangles 1 and 2 each have a 35° angle.

There's not enough information

case B) Triangles 3 and 4 are both isosceles. They each have a 40° angle.

There's not enough information (It is necessary to know if the given angle corresponds to the base angle or to the vertex angle in each triangle)

case C) Triangle 5 has a 30° angle and a 90° angle. Triangle 6 has a 30° angle and a  70° angle

The triangles are not similar, because the angles are not congruent

case D) Triangle 7 has a 50° angle and a 25° angle. Triangle 8 has a 50° angle and a  105° angle.

The triangles are congruent

Because

The measure of the angles in triangle 7 are 50°-25°-105° (remember that the sum of the interior angles in any triangle must be equal to 180 degrees)

The measure of the angles in triangle 8 are 50°-105°-25° (remember that the sum of the interior angles in any triangle must be equal to 180 degrees)

therefore

Both triangles have the same angles

That means

Triangles are similar

the answer is d

step-by-step explanation:

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: