Question

two triangles are similar if their corresponding angles are ____ and their corresponding sides are proportional.

the ____ theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

the proportionality property of similar triangles states that corresponding sides of similar triangles are ____.

in a right triangle, the altitude drawn to the hypotenuse creates two smaller triangles that are ____ to the original triangle and to each other.

the ____ theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

the ____ bisector divides the opposite side of a triangle into two segments proportional to the other two sides of the triangle.

in the midline theorem, the segment joining two midpoints in a triangle is ____ to the third side.

Explanation:

1. First Question

Step1: Recall similar triangles definition

By the definition of similar triangles, corresponding angles must be equal (congruent) for two triangles to be similar, along with corresponding sides being proportional.

Step1: Recall the midline theorem

The Midline Theorem (also called the Midsegment Theorem) states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Step1: Recall similar triangles proportionality

The proportionality property of similar triangles is that their corresponding sides are proportional (have the same ratio).

Answer:

equal (or congruent)

2. Second Question