- [Diff: 3]
- is an isoscelesright triangle[Diff: 3].
- Thereare manypossibleanswers.Hereis one: Auxiliarylines are in red:
a. is a parallelogram(in fact it is a rectangle)[Diff: 3].b. is a trapezoid[Diff: 3].c. is an isoscelestriangle[Diff: 3].ProvingQuadrilateralsare Parallelograms
LearningObjectives
- Provea quadrilateralis a parallelogramgivencongruentoppositesides.
- Provea quadrilateralis a parallelogramgivencongruentoppositeangles.
- Provea quadrilateralis a parallelogramgiventhat the diagonalsbisecteachother.
- Provea quadrilateralis a parallelogramif one pair of sidesis both congruentand parallel.
Introduction
You’ll rememberfrom earlierin this coursethat you havestudiedconversestatements.A conversestatement
reversesthe orderof the hypothesisand conclusionin an if-thenstatement,and is onlysometimestrue. For
example,considerthe statement:“If you studyhard,then you will get goodgrades.”Hopefullythis is true!
However, the converseis “If you get goodgrades,then you studyhard.”This may be true, but is it notnec-
essarilytrue—maybethereare manyotherreasonswhy you get goodgrades—i.e.,the classis reallyeasy!
An exampleof a statementthat is true and whoseconverseis also true is as follows:If I face east and then
turn a quarter-turnto the right,I am facingsouth.Similarly, if I turn a quarter-turnto the right and I am facing
south,then I was facingeast to beginwith.
Also all geometricdefinitionshavetrue converses.For example,if a polygonis a quadrilateralthen it has
four sidesand if a polygonhas four sidesthen it is a quadrilateral.