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 28°.

The flow chart with missing statements and reasons proves that the measure of angle ECB is 62°.

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

Base angle theorem
Corresponding angle are congruent
Measure of angle AED is 28°.

Alternate interior angles are congruent
Base angle theorem
Measure of angle AED is 62°.

Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 28°.>> my answer?

Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 62°.

Answer 1

the answer is D. I just took the exam.

Explanation:

Answer 2

(D)

Explanation:

Given: 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 28°.

To prove: The measure of angle ECB is 62°.

Proof:

Step1. Segment DE joins the mid points of segments AB and AC (GIVEN).

Step 2. Segment DE is parallel to segment BC (MIDSEGMENT THEOREM)

Step3. Angle ECB is congruent to angle AED (CORRESPONDING ANGLES ARE CONGRUENT) that is ∠AED≅∠ACB.

Step 4. Measure of angle DAE is 90° (Definition of right angle)

Step 5. Measure of angle ADE is 28° (Given)

Step 6. Thus, by triangle sum theorem, we have

∠DAE+∠ADE+∠AED=180°

∠AED=180-118

∠AED=62°

Step 7. Thus, by substitution, we have

∠AED≅∠ACB that is ∠ECB=62°

Hence proved.