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Mathematics, 03.02.2021 18:40 eddiewoods56881
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 68°.
Triangle ABC with segment DE. Angle ADE measures 68 degrees.
The following flowchart with missing statements and reasons proves that the measure of angle ECB is 22°:
Statement, Measure of angle ADE is 68 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 22 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 22 degrees, Reason, Substitution Property.
Which statement and reason can be used to fill in the numbered blank spaces?
Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 22°
Corresponding angles are congruent
Base Angle Theorem
Measure of angle AED is 68°
Alternate interior angles are congruent
Triangle Sum Theorem
Measure of angle AED is 22°
Alternate interior angles are congruent
Triangle Angle Sum Theorem
Measure of angle AED is 68°
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Triangle ABC is a right triangle. Point D is the midpoint of side AB, and point E is the midpoint of...
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