62 Tests for Parallelograms

1
6-2
Tests for Parallelograms
2
Theorem 6-5

• If both pairs of opposite sides of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.

Example
3
Theorem 6-6

• If both pairs of opposite angles of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.

Example
4
Theorem 6-7

• If the diagonals of a quadrilateral bisect each
  other, then the quadrilateral is a parallelogram.

example
5
Theorem 6-8

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

example
6
Definition

• Identifying Subgoals
• smaller steps needed to solve a larger problem

7
A quadrilateral is a parallelogram if the
following is true.-------------------------------
-------------------------1. Both pairs of
opposite sides are parallel.2.both pairs of
opposite sides are congruent.3.both pairs of
opposite angles are congruent.4.diagonals bisect
each other.5.a pair of opposite sides are both
parallel and congruent.
8
The coordinates of the vertices of quadrilateral
PQRS are P(-5,3), Q(-1,5), R(6,1), and S(2,-1).
Determine if quadrilateral PQRS is a parallelogram
Q
P
R
S