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-GEOMERY QUESTION-
*WILL AWARD BRAINLIEST FOR A CORRECT ANSWER*

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 47°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 43°

Which statement and reason can be used to fill in the numbered blank spaces?

a. Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 43°.

b. Alternate interior angles are congruent
Base angle theorem
Measure of angle AED is 47°.

c. Base angle theorem
Corresponding angle are congruent
Measure of angle AED is 43° .

d. Alternate interior angles are congruent
Triangle Sum Theorem
Measure of angle AED is 47°.

-GEOMERY QUESTION- *WILL AWARD BRAINLIEST FOR A CORRECT ANSWER* Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint class=
-GEOMERY QUESTION- *WILL AWARD BRAINLIEST FOR A CORRECT ANSWER* Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint class=

Answer :

KayKay2005
The answer is B. I used to do this type of stiff
lublana

Answer:

a.Corresponding angles are congruent

Triangle sum theorem

Measure of angle AED is [tex]43^{\circ}[/tex].

Step-by-step explanation:

We are given that a right triangle ABC. D is the midpoint of side AB and Point E is the midpoint of side AC.

The measure of angle ADE=[tex]47^{\circ}[/tex]

In triangle ADE

[tex]\angle ADE=47^{\circ}, \angle DAE=90^{\circ}[/tex]

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

By sum of angles of triangle property

[tex]47+90+\angle AED=180[/tex]

Substitute the given values

[tex]137+\angle AED=180[/tex]

[tex]\angle AED=180-137[/tex]

By subtraction property of equality

[tex]\angle AED=43^{\circ}[/tex]

[tex]\angle AED=\angle ECB[/tex]

Corresponding angles are congruent.

Therefore,[tex]\angle ECB=43^{\circ}[/tex].

Hence, option a is correct.

a. Corresponding angles are congruent

Triangle sum theorem

Measure of angle AED is [tex]43^{\circ}[/tex].

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