1. ## Proof Help

Given: PSTV is a parallelogram; PQ is congruent to RQ
Prove: Angle STV is congruent to angle R

Please see my attachment for the actual information.

Thank you in advance for any help. I cannot figure out how to work out this proof. I think I am confused because this incorporates both a parallelogram and a triangle.

Thank you!

2. ## Re: Proof Help

After reading through a couple other threads I promise I am not "too lazy" to work through this! I just have been staring at this for a while and I have come up with some ideas, but I just cannot seem to fit a proof together. Any help to get me started would be appreciated. I am thinking that I need to use a theorem for triangles, I just am not sure which would work.

3. ## Re: Proof Help

Originally Posted by vp1489
After reading through a couple other threads I promise I am not "too lazy" to work through this! I just have been staring at this for a while and I have come up with some ideas, but I just cannot seem to fit a proof together. Any help to get me started would be appreciated. I am thinking that I need to use a theorem for triangles, I just am not sure which would work.

Think isosceles triangle and parallel lines

4. ## Re: Proof Help

Any other hints? I am having a really hard time with proofs in general.

So I am guessing it will go something like this: PS is parallel to VT. And then I somehow need to prove that VT and TR are congruent, which would mean that angle V and angle R are congruent. Am I on the right track?

5. ## Re: Proof Help

Hello, vp1489!

It's simpler than that . . .

Given: PSTV is a parallelogram; PQ is congruent to RQ.
Prove: Angle STV is congruent to angle R.
Code:
              Q
o
* *
*   *
*     *
*       *
S o * * * * o T
*         * *
*         *   *
P o * * * * o * * o R
V

$PQ = RQ\quad\Rightarrow\quad \Delta PQR\text{ is isosceles} \quad\Rightarrow\quad \angle P = \angle R$

$\angle STV = \angle P\quad\text{Opposite angles of a parallelogram are equal.}$

$\therefore\:\angle STV \,=\,\angle R.$

6. ## Re: Proof Help

I really appreciate your help. I now understand everything up until the final step (I was focusing too much on the "smaller" triangles and did not even consider the large one)

Would you mind helping me understand that last step? Knowing the first few steps, I still do not completely understand how angle STV is equal to angle R.

Thank you in advance! This is very helpful to my understanding of this proof.