SWBAT… Agenda 1. Warm-up (10 min)2. Review HW (15 min)3. Notes on properties of parallelograms (20 min)

Warm-Up:1. 100 is 25% of what number?2. 23 is what percent of 115?3. Liz deposited $1,200 in a savings account

that pays 5¼% annually. How much would Liz have in her account after one year?

Thurs, 2/13

Pg. 364 – 365 #9 – 12, 14-16, 25-30, 38-40

SWBAT… use and apply the properties of parallelograms Agenda 1. Warm-up / Check HW (10 min)2. Review HW (15 min)3. 4 properties of parallelograms (20 min)

Warm-Up:1. 100 is 25% of what number?2. 23 is what percent of 115?3. As a realtor, you get a commission of 13% of your

sales profit. If the sales profit is $256,808, what is your commission?

4. Liz deposited $1,200 in a savings account that pays 5¼% annually. How much would Liz have in her account after one year?

Thurs, 2/13

HW: 2 Problems given at end of period

Properties of Parallelograms

Definition of a Parallelogram A parallelogram is a quadrilateral with both

pairs of opposite sides parallel. DC║AB and DA║CB. The symbol ABCD

is read “parallelogram ABCD.”

Property # 1 If a quadrilateral is a parallelogram, then

its opposite sides are congruent. AD BC and AB DC≅ ≅

Property # 2 If a quadrilateral is a parallelogram, then

its opposite angles are congruent.P ≅ R and Q ≅ S

P

Q R

S

Property # 3 If a quadrilateral is a parallelogram, then

its consecutive angles are supplementary.mP + mQ = 180°mQ + mR = 180° mR + mS = 180°mS + mP = 180°

P

Q R

S

Consecutive angles: Angles of a polygon that share a side (“next” to each other)

Consecutive angles are supplementary because they are same-side interior angles

Property # 4 If a quadrilateral is a parallelogram, then

its diagonals bisect each other. E is the midpoint of AC and BD, therefore AE

CE and DE BE ≅ ≅

ExamplesGiven HKLP. HK = _______ and HP = ________ .m< K = m<______ .m< L + m<______ = 180°.If m< P = 650, then m< H = ____, m< K = ____ and m< L =____.Given the diagonals with their point of intersection labeled M.If HM = 5, then ML = ____ .If KM = 7, then KP = ____ .If HL = 15, then ML = ____ .If m<HPK = 36°, then m<PKL = _____ .

H K

LP

PL KLP

P or K115° 65°

115°

M

5 units14 units7.5 units

36° (Alternate interior

angles are congruent.)

GUIDED PRACTICE

What property can you use to show that the quadrilateral is a parallelogram?

If two pairs of opposite sides are congruent, the quadrilateral is a parallelogram.

ANSWER

GUIDED PRACTICE

What property can you use to show that the quadrilateral is a parallelogram?

If the opposite angles are congruent, the quadrilateral is a parallelogram.

OR

If the consecutive angles are supplementary, the quadrilateral is a parallelogram.

ANSWER

Ex 1: Property #1

ExProperty #2

Ex.

Property #3

m JML

SOLUTION

By Theorem 8.5, the consecutive angle pairs in JKLM are supplementary. So, m KJM + m JML = 180°.

Because m KJM = 110°,m JML =180° –110° = 70°.

Find the indicated measure in JKLM.

Property #3

Ex 1: For what values of x and y must the figure be a parallelogram?

Property #3

Ex. In the given figure, AD and BC are diagonals of parallelogram gram ABCD.

A B

CD

O

1. If AO = 15 cm, how long is CO? Ans.( 15 cm )2. If DO is 18 cm, how long is BO?Ans. ( 18 cm )

Property #4

Solution:BS = TS9x – 4 = 7x +29x – 7x = 2 + 4 2x = 6 x = 3BS = 23, TS = 23

BT = 46

S

B A

TH

Ex 1: BS = 9x – 4 and TS = 7x + 2. Find BT

Property #4

Honors HW: For what values of x and y must the figure be a parallelogram?

Ex 1: Using properties of ParallelogramsFGHJ is a parallelogram. Find the unknown length. Explain your reasoning.

a. JHb. JK

Statement Reason

a. JH = FG Opposite sides of a are .≅ JH = 5 Substitute 5 for FG.

b. JK = GK Diagonals of a bisect each other.

JK = 3 Substitute 3 for GK

F G

J H

K

5

3

Ex 2: Using properties of parallelograms

PQRS is a parallelogram. Find the angle measure.Explain your reasoning.a. mRb. mQ Statement Reasona. mR = mP Opposite angles of a are .≅ mR = 70° Substitute 70° for mP.b. mQ + mP = 180° Consecutive s of a are supplementary.

mQ + 70° = 180° Substitute 70° for mP. mQ = 110° Subtract 70° from each side.

P

RQ

70°

S

Ex. 3: Using Algebra with Parallelograms

PQRS is a parallelogram. Find the value of x. Statement

mS + mR = 180°3x + 120 = 180

3x = 60x = 20

Consecutive s of a are supplementary.Substitute 3x for mS and 120 for mR. Subtract 120 from each side.Divide each side by 3.

S

QP

R3x°

120°

Reason