DO NOW Use the following diagram to solve

DO NOW Use the following diagram to solve: 1) x 2) y 3) x + y 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 1

WORKSHEET KEY 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 2

WORKSHEET KEY 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 3

WORKSHEET KEY 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 4

2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 5

PROPERTIES OF PARALLELOGRAMS Section 6 -2 Geometry Pre. AP, Revised © 2013 viet. dang@humble. k 12. tx. us 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 6

PROPERTIES OF PARALLELOGRAMS A. If a quadrilateral is a parallelogram, then its opposite sides are congruent 1. The opposite sides are congruent 2. The opposite angles are congruent 3. The consecutive angles are supplementary 4. The diagonals bisect each other 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 7

THEOREM 1 If a quadrilateral is a parallelogram, then its opposite sides are congruent. 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 8

THEOREM 2 If a quadrilateral is a parallelogram, then its opposite angles are congruent. 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 9

THEOREM 3 If a quadrilateral is a parallelogram, then its opposite angles are congruent. 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 10

THEOREM 4 If a quadrilateral is a parallelogram, then its diagonals bisect each other. 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 11

EXAMPLE 1 Find the value of x and y that ensure the quadrilateral is a parallelogram. y 6 x 4 x+8 y² 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 12

EXAMPLE 2 In Parallelogram CDEF, DE = 74 mm, DG = 31 mm, and m FCD = 42°. Find CF. 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 13

YOUR TURN In Parallelogram CDEF, DE = 74 mm, DG = 31 mm, and m FCD = 42°. Find DF. 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 14

EXAMPLE 3 WXYZ is a parallelogram. Find YZ. YZ = XW 8 a – 4 = 6 a + 10 2 a = 14 a=7 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 15

YOUR TURN WXYZ is a parallelogram. Find m Z. 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 16

EXAMPLE 4 Determine if the quadrilateral must be a parallelogram. Justify your answer. Yes. The 73° angle is supplementary to both its corresponding angles. 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 17

EXAMPLE 5 Determine if the quadrilateral must be a parallelogram. Justify your answer. No. One pair of opposite angles are congruent. The other pair is not. The conditions for a parallelogram are not met. 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 18

YOUR TURN Determine if the quadrilateral must be a parallelogram. Justify your answer. Yes. The diagonal of the quadrilateral forms 2 triangles. 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 19

EXAMPLE 6 PQRS is a parallelogram for x = 10 and y = 6. 5. Find m S and m R 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 20

EXAMPLE 7 Solve for x and y of MLPN 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 21

YOUR TURN Solve for a and c of MLPN 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 22

EXAMPLE 8 Three vertices of JKLM are J(3, – 8), K(– 2, 2), and L(2, 6). Find the coordinates of vertex M. L L K K M JJ The coordinates of vertex M are (7, – 4). 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 23

YOUR TURN Three vertices of PQRS are P(– 3, – 2), Q(– 1, 4), and S(5, 0). Find the coordinates of vertex R. 2/22/2021 2: 08 AM 6 -3: Conditions of Parallelograms 24

VIDEO http: //www. youtube. com/watch? v=Rpkjb 4 Tx 844 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 25

ASSIGNMENT Pg 395: 15 -24, 32 -43, 46, 47 Pg 402: 11 -15, 20 -23 2/22/2021 2: 08 AM 6 -1: Intro to Quadrilaterals 26