Session 31 Check your homework with a neighbor.

Which property justifies the statement?

1. If A B and B C, then A C.

2. If M N, then N M.

3. If 1 = 80, and m1 = m2, then m2 = 80.

Transitive property of congruence

Symmetric property of congruence

Substitution property of equality

AGENDA

1. Discuss hw

2. Notes 6.2 & 6.3

3. Practice

Fri. 11th

Quiz & 6.4

Tues. 14th

6.5 & 6.6

Thurs. 16th

6.7

HW Check1. Use the number of sides to

identify the polygon.

2. Is #1 concave or convex, explain your answer.

3. Use the information in the diagram to find the mA.

4. Use the information in the diagram to solve for x.

Concave A37

153

8x 3x – 1

2x + 13

143

15

Nonagon

Questions over your hw?p. 325 1 - 30, 37 - 39, 41 - 46

6.2 Properties of Parallelograms

Parallelogram• A quadrilateral with both pairs of opposite sides parallel

IF a quadrilateral is a parallelogram then…

• Opposite sides are congruent

(THM 6.2)

Opposite sides are congruent

IF a quadrilateral is a parallelogram then…

• Opposite angles are congruent

(THM 6.3)

Opposite angles are congruent

IF a quadrilateral is a parallelogram then…

• Consecutive angles are supplementary

(THM 6.4)

Consecutive angles are supplementary.

ADD UP TO 180°

IF a quadrilateral is a parallelogram then…

• Diagonals bisect each other

(THM 6.5)

Diagonals bisect each other.

This cuts the diagonals into two equal parts.

ABCD is a parallelogram. Find the lengths and the angle measures.

1. AD

2. EC

3. mADC

4. mBCD

B 8 C

A D

6545

E

5

85

110

70

5. Find the value of each variable in the parallelogram.

4y

x = 5

2y42x – 6

y = 30

6. Find the value of each variable in the parallelogram.

10x = 6

3y + 12x – 1

y = 3 x + 5

6.3 Proving Quadrilaterals are Parallelograms

How do you know if you have one?

1.BOTH pairs of opposite sides are parallel2.BOTH pairs of opposite sides are congruent

3. BOTH pairs of opposite angles are congruent

4.ONE angle is supplementary to BOTH consecutive angles

5.diagonals BISECT each other

6. ONE pair of opposite sides are CONGRUENT & PARALLEL

60 120

120

6 6

50°

130°

Show that A(2, 0), B(3, 4), C(-2, 6), and D(-3, 2) is a parallelogram.

• One way is to show that opposite sides are parallel by finding every sides’ slopes.

• Another way is to find the distances of both pairs of opposite sides.

Show that A(2, 0), B(3, 4), C(-2, 6), and D(-3, 2) is a parallelogram.

• Let’s find the slopes of all sides.

ABm 4

CDm 4

BCm 5

2

DAm 5

2

Since opposite sides have the same slope,

opposite sides are parallel.

ABCD IS a parallelogram!!

Practice•WS 6.2 A #1 – 21

•WS 6.3 A #1 – 14

HW•P. 334 #21 – 37 odd

•P. 342 #2 – 8, 17 – 19 all