Warm Up: Day 2

Find the coordinates of point M in parallelogram PRAM.

A(b, c)

R(a, 0)

M(__, __)

P.

1. Determine the values of the variables for which, the figureto the right is a parallelogram.

Find all possible coordinates of vertex D of parallelogram ABCD.

• A (2,0), B(3,4), C(-2,6)

Ch. 6.3: Proving Quadrilaterals are

Parallelograms

Students will justify that a quadrilateral is a parallelogram

Given: Prove: ABCD is a parallelogram.€

AB ≅ CD,AD ≅ CB A B

CD

Theorem 6.6 If both pairs of opposite sides of a quadrilateral are congruent, then the

quadrilateral is a parallelogram.

Theorem 6.7 If both pairs of opposite angles of a quadrilateral are congruent, then the

quadrilateral is a parallelogram.

Theorem 6.8 If an angle of a quadrilateral is supplementary to both of its consecutive

angles, then the quadrilateral is a parallelogram.

Theorem 6.9 If the diagonals of a quadrilateral bisect each other, then the quadrilateral

is a parallelogram.

Given: Prove: ABCD is a parallelogram.€

BC //DA,BC ≅ DAC

B

A

D

Theorem 6.10

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

Practice ProblemsStudy the markings on each figure and decide

whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

1. 3.

2.

D C

BA 12

12

88

9

9 C

BA

D

A

B

D

C

1100

700

700

Let’s ReviewWays to Prove a Shape is a Parallelogram:• Show that both pairs of opposite sides are parallel• Show that both pairs of opposite sides are

congruent• Show that both pairs of opposite angles are

congruent• Show that one angle is supplementary to both

consecutive angles• Show that the diagonals bisect each other• Show that one pair of opposite sides are congruent

and parallel

Quiz tomorrow on 6.1-6.3