Question

given ; SV is parallel to TU and SVX is congurent to UTX
Prove: VUTS is a parallelogram

Answer 1

http://assets.openstudy.com/updates/attachments/50cfa3a7e4b0031882dcf7a3-stewie-1355787831736-456845131201185029am1712747141.png

Answer 2

http://assets.openstudy.com/updates/attachments/50cfa3a7e4b0031882dcf7a3-stewie-1355787832049-456845131201185027am661749930.png

Answer 3

http://assets.openstudy.com/updates/attachments/50cfa3a7e4b0031882dcf7a3-stewie-1355787862098-456845131201185026am1782080347.png

Answer 4

Two ways of proving a quadrilateral is a parallelogram are:
1. Show that one pair of opposite sides is both parallel and congruent.
2. Show that both pairs of opposite sides are parallel.

In this case, you have a pair of sides already given as parallel.
Those two sides are corresponding parts of two triangles that are given as congruent.
It's easy to show that the sides are congruent. Then by the first method above you can prove that the quadrilateral is a parallelogram.

Answer 5

I still don't understand though..... @mathstudent55

Answer 6

Let's go back a few steps.
A triangle is a 3-sided figure, whose sides are line segments. I'm sure you're familiar with triangles. Triangles are examples of a 3-sided polygon. A polygon is a figure that is made up of line segments joined at the endpoints, and the segments do not cross each other.
If instead of having 3 sides, you have 4 sides, then the figure is called a quadrilateral. Any 4-sided polygon is a quadrilateral. There are some quadrilaterals that have special names. One such type of a quadrilateral is called a parallelogram. The definition of a parallelogram is: A parallelogram is a quadrilateral that has two pairs of opposite sides parallel.
This means that if in a problem you are told as given that a quadrilateral is a parallelogram, you can conclude form the given information and the definition of a parallelogram that the opposite sides are parallel.
A definition also works backwards. That means that if you can show that in a quadrilateral, both pairs of opposite sides are parallel, you can conclude the quadrilateral is a parallelogram.
In geometry there are statements that are held to be true but cannot be proved. These statements are called axioms or postulates. They can be used in proofs. They can only be used in the way they are stated. They do not necessarily and automatically work backwards like definitions do.
Then there are also theorems. A theorem is a statement that can be proved. Similarly to axioms or postulates, thorems can only be used in the way they are stated.
Now let's look at parallelograms. There is a theorem that states that in a parallelogram, opposide sides are congruent. Remember, that unlike a definition, a theorem does not automatically work backwards, so just because you know that if a quadrilateral is a parallelogram, opposite sides are congruent, that does not mean that if you have a quadrilateral with opposidte sides congruent you can say it's a parallelogram. The only way to be able to say so would be to have this new statement as a new theorem. Interestingly enough, this can be proved and there is such a statement. There is a thorem that states that if in a quadrilateral both pairs of opposite sides are congrunt, the quadrilateral is a parallelogram.
Then there is another theorem that states that if in a quadrilateral, two opposite sides are both parallel and congruent, the quadrilateral is a parallelogram. This is the theorem that can be used in this problem to prove that VUTS is a parallelogram.
Go over this and let me know if you understand it better now. Then we'll work on the actual proof.