Question

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 36°.

The following flowchart with missing statements and reasons proves that the measure of angle ECB is 54°:

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

Answer 1

1.Measure of angle AED is 36°
2.Base Angle Theorem
3.Corresponding angles are congruent
1.Measure of angle AED is 54°
2.Base Angle Theorem
3.Alternate interior angles are congruent
1.Measure of angle AED is 54°
2.Triangle Sum Theorem
3.Alternate interior angles are congruent
1.Measure of angle AED is 54°
2.Triangle Sum Theorem
3.Corresponding angle are congruent

Answer 2

Help me @hero

Answer 3

whats the question?

Answer 4

the question is already up there @Jack1

Answer 5

From the picture: this doesnt match up:

1.Measure of angle AED is 36°
2.Base Angle Theorem
3.Corresponding angles are congruent

AED cant be 36, as ADE is 36 and the other angle is 90

Answer 6

What's the answer then @Jack1

Answer 7

if lines DE and BC are parallel: the triangle is congruent
nothing in the picture indicates whether they are or are not parallel... so we can't assume they are... so ... yeah, i don't know how to solve it, sáll

Answer 8

i'd answer: not enough data

Answer 9

wait: ur 2nd picture indicates they're parallel (the flow diagram)

Answer 10

yeah @Jack1

Answer 11

as they're parallel: angle ADE = angle ABC
and angle AED = ACB
so they're congruent

Answer 12

AED = 54
ACB = 54
ADE = 36
ABC = 36
they share an angle of 90
so ... yeah

Answer 13

what is the answer? @Jack1

Answer 14

u tell me @Bacon211
are the corresponding angles congruent?
or the alternate interior angles congruent?
once you understand this you can chose ther right answer

Answer 15

Corresponding @Jack1

Answer 16

cool, so as they're corresponding angles, i'd pick this one:

1.Measure of angle AED is 54°
2.Triangle Sum Theorem
3.Corresponding angle are congruent

Answer 17

I'm correct? @Jack1

Answer 18

i think so

Answer 19

trust me... its that one i said... probably...

Answer 20

... i think... maybe...?

Answer 21

Thanks @jack1

Answer 22

The answer is D:
AED is 54
Triangle Sum theorem
Corresponding angles

Answer 23

sweeet ;)