The statement and reason that can be used to fill the numbered blank spaces is the fourth option
- Measure of angle AED is 54°
- Triangle Sum Theorem
- Corresponding angles are congruent
The statement and reasons are presented as follows;
Segment DE joins the midpoints of segments AB and AC; Given
Segment DE is parallel to segment BC; Midsegment Theorem
Measure of angle ADE is 36°; Given
Measure of angle DAE is 90°; Definition of right Angle
1. Measure of angle AED is 54°; 2. Triangle sum theorem
Angle ECB is congruent to angle AED; 3. Corresponding angles are congruent
Measure of angle ECB is 54°; Substitution property
The triangle sum theorem states that the sum of the interior angles in a triangle is 180°, therefore; m∠AED + m∠ADE + m∠DAE = 180°
m∠AED + = 180°
m∠AED = 180° - (36° + 90°)
m∠AED = 54°
The corresponding angles theorem states that the corresponding angles formed between parallel lines and their transversal are congruent
Angle ∠ECB and angle ∠AED are corresponding angles, therefore;
Angle ECB is congruent to angle AED
m∠ECB = m∠AED (Definition of congruent angles)
The substitution property states that if A = B then B can substitute A in a specified equation and the equation remain valid
m∠AED = 54° and m∠ECB = m∠AED, therefore, m∠ECB = 54°
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