Download Proving Parallelograms

January 23, 2017
Unit 7, Lesson 4
Proving
Parallelograms
The more things change, the more they are the same.
- Alphonse Karr
We currently only have one way to show a
quadrilateral is a parallelogram: the definition (two
pairs of parallel sides)
As you have seen parallelograms have lots of
properties so they can be very useful. Let's explore
some other ways to show a quadrilateral must be a
parallelogram.
January 23, 2017
Example 1:
In quadrilateral ABCD, AB = CD and BC = AD. Show quad. ABCD
must be a parallelogram.
(Hint: what is the definition of a parallelogram?)
Example 2:
In quadrilateralWXYZ,
(Hint: you do not need to draw a diagonal. What is the angle sum of a quadrilateral?)
January 23, 2017
What are some other ways to show a quadrilateral is a parallelogram?
Example 3:
January 23, 2017
Example 4:
Ways to Show a Quadrilateral is a Parallelogram:
1. Show both pairs of opposite sides are parallel
(def. of a parallelogram)
2. Show both pairs of opposite sides are congruent
(theorem 5-4)
3. Show both pairs of opposite angles are congruent
(theorem 5-6)
4. Show the diagonals bisect each other.
(theorem 5-7)
5. Show one pair of opposites are congruent
and parallel. (theorem 5-5)
6. Show consecutive angles are supplementary
(relates back to def. of a parallelogram)
January 23, 2017
Can you find any other combinations that will
show a quadrilateral is a parallelogram?
Why does it seem parallelograms are so important in Geometry?
January 23, 2017