Therefore The Missing reason is
Triangle Sum Theorem.
Step-by-step 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 ∠ADE is 47°.
To Prove
measure of ∠ECB is 43°.
Proof:
Triangle Sum Theorem :
The Triangle Sum Theorem states that the three interior angles of any triangle add up to 180 degrees.
∴ 90 + 47 + m∠AED = 180°
∴ m∠AED = 180 - 137 = 43°
Statement Reason
m∠ADE = 47° = Given
m∠DAE = 90° = Definition of a right angle
m∠AED = 43° = Triangle Sum Theorem
segment DE joins the midpoints of segment AB and segment AC =Given
segment DE is parallel to segment BC =Midsegment of a Triangle Theorem
∠ECB ≅ ∠AED =Corresponding angles are congruent
m∠ECB = 43° =Substitution property
Therefore The Missing reason is
Triangle Sum Theorem
Below are the correct choices:
Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 43°.
Alternate interior angles are congruent
Base Angle Theorem
Measure of angle AED is 47°
Base Angle Theorem
Corresponding angle are congruent
Measure of angle AED is 43°.
Alternate interior angles are congruent
Triangle Sum Theorem
Measure of angle AED is 47°
The answer is the 3rd one. I hope it helps.
Step-by-step explanation:
sdfghj
Step-by-step explanation: