3. Proving That a Quadrilateral Is a Parallelogram
Sign In
See solution.
First let's recall the Opposite Sides Parallel and Congruent Theorem.
|
Opposite Sides Parallel and Congruent Theorem |
|
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. |
Therefore, to use this theorem we need to construct a pair of segments that will be congruent and parallel. After that we will connect the endpoints of the segments to form a quadrilateral. Let's start with drawing a segment AB.
Next we will draw a line l that is parallel to AB.
Now we will choose a point D that lines on our line.
Using the compass, we will copy the length of AB. Then we will put the compass at D and draw an arc intersecting l.
The point of intersection of the arc and the line will be the fourth vertex. Let's label it C.
Finally we will connect the endpoints of our parallel and congruent segments to form a quadrilateral ABCD.
By the Opposite Sides Parallel and Congruent Theorem we can state that ABCD is a parallelogram. Notice that this is just one example of a parallelogram we could make using the theorem.