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?

Answer 1

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

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

1. Corresponding angles are congruent
2. Triangle Sum Theorem
3. Measure of angle AED is 28°.

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

Answer 2

1. I would look at the position of the angles with respect to our parallel lines (See the previous statement before 1.). Both of these angles are in the same place where the transversal intersects the parallel lines. This \(correspondence\) between them means that they are congruent.

Answer 3

I'm going to skip 2. and come back to it after 3.

3.. Since we just proved that angle ECB and angle AED are congruent, we would imagine there is a purpose for doing so, right? We can look back at angle AED to see what we know about it. We're proving that the measure of angle ECB is equal to 62, and AED is congruent to ECB. So, AED would the the same angle.


2. The justification for this comes in the fact that AED is the only missing angle in triangle ADE. There is a theorem that states that the sum of the interior angles of a triangle always add up to 180, and this would be a good application.