Provinga Quadrilateralis a ParallelogramGivenCongruentOppositeAngles
Muchlike the conversestatementsyou studiedaboutoppositeside lengths,if you can provethat opposite
anglesin a quadrilateralare congruent,the figureis a parallelogram.
Example 2
Completethe two-columnproofbelow.- Given:Quadrilateral with and
- Prove: is a parallelogram
Statement Reason- is a quadrilateral with 1. Given
and
2.2. Sumof the anglesin a quadrilateralis
3. Substitution and
3.
- Combinelike terms
- Factoring
- Divisionpropertyof equality(dividedboth
sidesby 2)
6.
- If interiorangleson the sameside of a
- transversalare supplementarythen the lines
crossedby the transversalare parallel
- Substitutionon line 6