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 47°.

Triangle ABC with segment DE. Angle ADE measures 47 degrees.

The following flowchart with missing statements and reasons proves that the measure of angle ECB is 43°:

Statement, Measure of angle ADE is 47 degrees, Reason, Given, and Statement, Measure of angle DAE is 90 degrees, Reason, Definition of right angle, leading to Statement 3 and Reason 2, which further leads to Statement, Measure of angle ECB is 43 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 1, which further leads to Statement, Measure of angle ECB is 43 degrees, Reason, Substitution Property.

Which statement and reason can be used to fill in the numbered blank spaces? (1 point)

1. Corresponding angles are congruent
2. Triangle Sum Theorem
3. Measure of angle AED is 43°

1. Alternate interior angles are congruent
2. Base angle theorem
3. Measure of angle AED is 47°

1. Base angle theorem
2. Corresponding angle are congruent
3. Measure of angle AED is 43°

1. Alternate interior angles are congruent
2. Triangle Sum Theorem
3. Measure of angle AED is 47°

Answer 1

any idea ?

- first of all try drawing this right triangle ABC and these points of D and E