Example 2
Completion requirements
Example 2
Given: \(\triangle\)ABC 
\(\triangle\)EDC
Prove: ABED is a parallelogram
This proof will require a few steps. It may be a good idea to begin by working on your diagram, labelling any sides or angles you know are equal. Once you have determined enough information, you can organize it into a more formal proof like the one below.
| Statement | Justification | Diagram |
|---|---|---|
| \(\angle\)BAC = \(\angle\)DEC | They are corresponding angles of congruent triangles. |  |
| AB || DE | Alternate interior angles are equal. |  |
| AC = EC | They are corresponding sides of congruent triangles. |
|
| DC = BC | They are corresponding sides of congruent triangles. |  |
| \(\angle\)ACD = \(\angle\)BCE | They are opposite angles. |  |
| \(\triangle\)ACD \(\triangle\)ECB |
SAS |  |
| \(\angle\)CAD = \(\angle\)CEB | They are corresponding angles of congruent triangles. |  |
| AD || BE | Alternate interior angles are equal. |  |
| ABED is a parallelogram. |
ABED is a quadrilateral with two pairs of parallel sides. |  |
