# congruent triangles

##### Full Member
Yes, the triangles in the figure are congruent.
<U = <Y
W is the midpoint of UY.
VWU = XWY
UW = YW
UW = XW

Does that mean name the theorem or postulate that proves the congruence?

#### Subhotosh Khan

##### Super Moderator
Staff member
View attachment 15025Yes, the triangles in the figure are congruent.
<U = <Y
W is the midpoint of UY.
VWU = XWY
UW = YW
UW = XW

Does that mean name the theorem or postulate that proves the congruence?
How is that?

#### Jomo

##### Elite Member
There are a few statements that you said that concerns me. But I will not comment on them (yes, this is Jomo).
You need to decide on your strategy. You have a side and an angle that corresponds. So what would you also like to be congruent? DO NOT look at the diagram to answer my question. Once you answer this question, then see if it is true.

#### topsquark

##### Full Member
View attachment 15025Yes, the triangles in the figure are congruent.
<U = <Y
W is the midpoint of UY.
VWU = XWY
UW = YW
UW = XW

Does that mean name the theorem or postulate that proves the congruence?
I think you mean VW = XW. But you can't say that directly because there is no reason we can make the assumption that W bisects VX.

But...

Hint: Look at the angles UWV and YWX.

-Dan

##### Full Member
There are a few statements that you said that concerns me. But I will not comment on them (yes, this is Jomo).
You need to decide on your strategy. You have a side and an angle that corresponds. So what would you also like to be congruent? DO NOT look at the diagram to answer my question. Once you answer this question, then see if it is true.
side angle side?

#### lev888

##### Senior Member
side angle side?
And why does an answer end with a question mark?

#### pka

##### Elite Member
Looking at the given: $$\displaystyle \angle VUW \cong \angle WYX,~\&~\overline{UW}\cong\overline{WY}$$.
Again, those are given. You should see that $$\displaystyle \angle VUW \cong \angle WYX$$. WHY?
Then
$$\displaystyle \Delta UWV\cong \Delta YWX$$ by $$\displaystyle ASA$$ WHY?

#### Jomo

##### Elite Member
side angle side?
side angle side or angle side angle. Now which one can you easily get. In sas which sides do you need to be congruent? Are they congruent? In asa which angles do you need to be congruent? Are they congruent?
This is the logic you need to use for these type problems!

##### Full Member
side angle side or angle side angle. Now which one can you easily get. In sas which sides do you need to be congruent? Are they congruent? In asa which angles do you need to be congruent? Are they congruent?
This is the logic you need to use for these type problems!
ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

#### Jomo

##### Elite Member
So do you have asa or sas?

#### Jomo

##### Elite Member
So which angles are you saying are congruent that was not given?

##### Full Member
So which angles are you saying are congruent that was not given?
UW = WY

#### Jomo

##### Elite Member
That is not a good answer as they are NOT angles but rather sides. To make things worse, they are already given and are part of the asa. You need to find the angles that are congruent but NOT the ones given. For the record, you already found another pair of congruent angles in a previous post.

##### Full Member
That is not a good answer as they are NOT angles but rather sides. To make things worse, they are already given and are part of the asa. You need to find the angles that are congruent but NOT the ones given. For the record, you already found another pair of congruent angles in a previous post.
<V = <X

#### lev888

##### Full Member
Based on what?
I don’t understand what angles I’m suppose to find.

#### Subhotosh Khan

##### Super Moderator
Staff member
I don’t understand what angles I’m suppose to find.
The original post asked you to PROVE that the triangles UVW and WXY are congruent

Did you do that?

If yes, how (in which post) and what theorem did you use to prove that?