Question

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) corresponding angles are congruent
2) triangle sum theorem
3) measure of angle aed is 43°
4) alternate interior angles are congruent
5) base angle theorem
6) measure of angle aed is 47°

Answer 1

To fill in the numbered blank spaces, we can use the following statement and reason: angle ECB is congruent to angle AED, and the reason is alternate interior angles are congruent. Another statement and reason that can be used are: Measure of angle ECB is 43 degrees, and the reason is substitution property.

Step-by-step explanation:

Based on the information provided, we can fill in the numbered blank spaces as follows:

Statement: Angle ECB is congruent to angle AED

Reason: Alternate interior angles are congruent

Statement: Measure of angle ECB is 43 degrees

Reason: Substitution property

Statement: Segment DE is parallel to segment BC

Reason: Midsegment theorem