Warm-Up

1
Warm-Up

• Each section of glass in the exterior of a
  building in Macau, China, forms an equilateral
  triangle. Do you think the window washers feet
  stay parallel to the ground as he lands at each
  level of windows? Explain. (Assume the bases of
  the lowest triangles are parallel to the ground)

2
Section 6.3 Proving that a Quadrilateral is a
Parallelogram
3
Properties of Parallelograms

• If a quadrilateral is a parallelogram then
• Opposite sides are parallel
• Opposite sides are congruent
• Opposite angles are congruent
• Consecutive angles are supplementary
• Diagonals bisect each other

4
Ways to Prove a Quadrilateral is a Parallelogram

• If a quadrilateral has opposite sides that are
  parallel
• If a quadrilateral has opposite sides that are
  congruent
• If a quadrilateral has opposite angles that are
  congruent
• If a quadrilateral has diagonals that bisect each
  other
• Then it is a parallelogram!

5
Be Careful!

• If a quadrilateral has an angle that is
  supplementary with both of its consecutive angles
  then it is a parallelogram!
• So. Youll need to check that it is
  supplementary to the angles on both sides of it

6
Example

• Are you given enough information to determine
  whether the quadrilateral is a parallelogram?

7
Example

• Are you given enough information to determine
  whether the quadrilateral is a parallelogram?

8
Example

• Are you given enough information to determine
  whether the quadrilateral is a parallelogram?

9
Theorem 6.12

• If one pair of opposite sides of a quadrilateral
  are congruent and parallel then the quadrilateral
  is a parallelogram

10
Example

• For what value of y must PQRS be a parallelogram?

11
Example

•  

12
Example

• A truck sites on the platform of a vehicle lift.
  Two moving arms raise the platform until a
  mechanic can fit underneath. Why will the truck
  always remain parallel to the ground as it is
  lifted?

13
Homework

• 6.3 Worksheet