Triangle abc is a right triangle. point d is the midpoint of side ab, and point
the table info is below.
statement reason
m∠ade = 47° =given
m∠dae = 90° =definition of a right angle
m∠aed = 43° =?
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
which theorem can be used to fill in the missing reason?
concurrency of medians theorem
isosceles triangle theorem
triangle inequality theorem
triangle sum theorem
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:
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Step-by-step explanation:
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