Question

Question 10(Multiple Choice Worth 1 points)
(02.05 MC)

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.

The following flowchart with missing statements and reasons proves that the measure of angle ECB is 54°:

Statement, Measure of angle ADE is 36 degrees, Reason, Given, and Statement, Measure of angle DAE is 90 degrees, Reason, Definition of right angle, leading to Statement 1 and Reason 2, which further leads to Statement, Measure of angle ECB is 54 degrees, Reason, Substitution Property. Statement, Segment DE joins the midpoints of segment AB and AC, Reason, Given, leading to Statement, Segment DE is parallel to segment BC, Reason, Midsegment theorem, which leads to Angle ECB is congruent to angle AED, Reason 3, which further leads to Statement, Measure of angle ECB is 54 degrees, Reason, Substitution Property.

Which statement and reason can be used to fill in the numbered blank spaces?


Measure of angle AED is 36°
Base Angle Theorem
Corresponding angles are congruent

Measure of angle AED is 54°
Base Angle Theorem
Alternate interior angles are congruent

Measure of angle AED is 54°
Triangle Sum Theorem
Alternate interior angles are congruent

Measure of angle AED is 54°
Triangle Sum Theorem
Corresponding angles are congruent

Answer 1

Answer:

To fill in the blank spaces, we need to consider the properties of angles formed by parallel lines and a transversal. In this case, angle AED is formed by DE, which is parallel to BC.

Statement 1: Measure of angle AED is 54°

Reason 2: Triangle Sum Theorem

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is 180 degrees. Since angle DAE is a right angle (given), angle AED must be complementary to it, making it also 90 degrees. Therefore, the measure of angle AED is 54 degrees.

So, the correct option is:

Measure of angle AED is 54°

Triangle Sum Theorem