Geometry Triangle Congruence - Should be easy?

For #3, you can say an angle is bisected when a line or segment divides the angle into two equal parts.
  • #1
luke8ball
22
0
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!
 

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  • #2


luke8ball said:

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.
 
  • #3
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!
 
  • #4
luke8ball said:
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 .
 

Related to Geometry Triangle Congruence - Should be easy?

What is the definition of triangle congruence?

Triangle congruence is the term used to describe two triangles that have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal.

What are the different methods for proving triangle congruence?

The three main methods for proving triangle congruence are SSS (side-side-side), SAS (side-angle-side), and ASA (angle-side-angle). These methods use a combination of corresponding sides and angles to show that the triangles are congruent.

What types of transformations preserve triangle congruence?

The transformations that preserve triangle congruence are translation, reflection, and rotation. This means that if you move, mirror, or rotate a triangle, the resulting triangle will still be congruent to the original.

What is the difference between congruent triangles and similar triangles?

Congruent triangles have the same size and shape, while similar triangles have the same shape but different sizes. In similar triangles, the corresponding sides are proportional, but in congruent triangles, they are equal.

What real-life applications use triangle congruence?

Triangle congruence is used in various fields such as architecture, engineering, and design. For example, in construction, congruent triangles are used to ensure that structures are stable and identical. In art and design, congruent triangles are used to create symmetrical and visually appealing compositions.

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