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 28°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 62°: Which statement and reason can be used to fill in the numbered blank spaces?

Iwould think its Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 28°

I hope I helped

Brainliest would be appreciated

Have a great day!

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lublana lublana · Answer 2 · 2019-06-27T12:55:23+02:00

Answer:

Because [tex]\angle ECB=62^{\circ}= \angle ADE[/tex] ( coresponding angles are equal )

Step-by-step explanation:

Given triangle ABC is a right triangle.

It means one angle of triangle ABC is of[tex]90^{\circ}[/tex].

[tex]\angle mA=90^{\circ}[/tex]

D is the mid point of side AB and E is the mid point of side AC.

Meet D to E . Now DE[tex]\parallel[/tex]BC

In triangle ADE

[tex]m\angle ADE=28^{\circ}[/tex] ( given )

[tex]m\angle DAE=90^{\circ}[/tex] ( given)

Now,

Statement : [tex]m\angle ADE+ m\angle DAE +m\angle AED=180^{\circ}[/tex].

Reason: Angle sum property of traingle.

Statement: [tex]28^{\circ}+ 90^{\circ} + m\angle AED = 180^{\circ}[/tex]

Reason: By using substitution property .

Statement: [tex]\angle AED=62^{\circ}[/tex]

Reason: By usin subtarction property of equality.

Statement: [tex]m\angle AED=m\angle ECB=62^{\circ}[/tex]

Reason: Corresponding angles are congruent when transversal line intersect two parallel lines.

Hence proved.