Question

In the figure below, segment CD is parallel to segment EF and point H bisects segment DE


Prove ΔDIH ≅ ΔEGH.

Answer 1

Someone plsss

Answer 2

@nikato I said they were congruent by the asa postulate

Answer 3

DH=EH Definition of a Bisector
Angle IDH = angle GEH Alternate interior angles
Angle DHI = angle EHG Vertical angles are congruent
Triangle DIH = Triangle EGH ASA postulate

Answer 4

Does that make sense?

Answer 5

Yup. Great job!

Answer 6

Thank you but one more thing

Answer 7

Sarah walks 20 feet away from her house and places a mirror on the ground. She backs 5 feet away from the mirror so that she can see the tip of the roof. Sarah's eyes are 4 feet above the ground. The angles between the top of the house, the mirror, and the ground and between Sarah's eyes, the mirror, and the ground are congruent as shown in the image:

Answer 8

Prove the triangles are similar.

Answer 9

I know you use the AA postulate not sure how though.

Answer 10

Wait, are the two angles marked in the diagram congruent?

Answer 11

I believe so

Answer 12

I'm not really sure how to prove. I guess I'm kinda assuming this

Answer 13

But the house should be perpendicular to the ground, making it a right angle

Answer 14

And same thing with the person, and since right angles are congruent, u can use AA

Answer 15

Thanks, I was thinking the same thing, but needed some reassurance. Thanks a lot! :)))))

Answer 16

Yea, I think that's the only thing u can do with the info u were given

Answer 17

Ye

Answer 18

Thanks again

Answer 19

No problem

Answer 20

@rumunerocks I'm going to close this question if that's ok with you.

Answer 21

no wait whats the height of the house then

Answer 22

If you want to find the height, set up a proportion becuz u already know the two triangles are similar.

4. x
--= -----
5. 20

Solve for x