Geometry Triangle Congruence - Should be easy?

[luke8ball]

Geometry Triangle Congruence - **Edited to include diagram**

Homework Statement

Hi! The three simple geometry problems are in the attached photo. Sorry if they're difficult to read. I haven't seen this information in so long, and could use some help. :D

Can you use the given information to determine that (AB) = (BC) ̅? Justify your answer.

The Attempt at a Solution

1. I would say that we cannot conclude AB = BC, because we have ***, which you can't conclude anything from.

2. Yes, AB = BC, because we have two right triangles, BE = BE, and AE = EC. Thus the hypotenuses must be the same?

3. I feel like the answer is yes here. Can one say that BD bisects angle ABC? Therefore, we have ASA?

Thanks a lot guys/girls!

 

[SammyS]

Homework Statement

Hi! The three simple geometry problems are in the attached photo. Sorry if they're difficult to read. I haven't seen this information in so long, and could use some help. :D

Can you use the given information to determine that (AB) = (BC) ̅? Justify your answer.

The Attempt at a Solution

1. I would say that we cannot conclude AB = BC, because we have ***, which you can't conclude anything from.

2. Yes, AB = BC, because we have two right triangles, BE = BE, and AE = EC. Thus the hypotenuses must be the same?

3. I feel like the answer is yes here. Can one say that BD bisects angle ABC? Therefore, we have ASA?

Thanks a lot guys/girls!

You are correct. Answers are: no, yes, yes.

For #1 you haven't given a reason.

For # 3, how do you know the the angle is bisected? BTW: You could have used SAS immediately.

 

[luke8ball]

Thanks Sammy!

For #1, I apparently typed a banned word via the abbreviation for angle-side-side. Whoops!

Is that a legitimate reason now to say no?

Also, for #3, I see now that the angle bisection comment is irrelevant and not necessarily justified either. When can you say that an angle is bisected?

Thanks again!

 

[SammyS]

Thanks Sammy!

For #1, I apparently typed a banned word via the abbreviation for angle-side-side. Whoops!

Is that a legitimate reason now to say no?

Also, for #3, I see now that the angle bisection comment is irrelevant and not necessarily justified either. When can you say that an angle is bisected?

Thanks again!

Yes, for #1 A$$ is as good as SSA .