Question

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 36°. Triangle ABC with segment DE. Angle ADE measures 36 degrees. Which theorem can be used to fill in the missing reason?

a. Concurrency of Medians Theorem
b. Isosceles Triangle Theorem
c. Midsegment of a Triangle Theorem
d. Triangle Inequality Theorem

Answer 1

The missing reason can be filled by using the Midsegment of a Triangle Theorem, which states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

Step-by-step explanation:

The missing reason can be filled by using the Midsegment of a Triangle Theorem. According to this theorem, the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. In this case, segment DE connects the midpoints of sides AB and AC of triangle ABC. Therefore, DE is parallel to BC and half its length. Hence, we can use the Midsegment of a Triangle Theorem to fill in the missing reason.