Pre-AP Geometry Worksheet 5.8

Pre-AP Geometry Name: ___________________ Worksheet 5.8: Properties of Parallelograms Date: _______ Period: ____ I. In exercises 1 - 6, the quadrilateral is a parallelogram. Find the indicated measures. (Show work)

1) a______ b______ c _____ 2) m�CDA = 100°; m�DCE = 35°; m�DAE = 5x; m�EAB = 6y + 5 d______ e______ f ______ x_______ y____

3) m�ADE = x - y; m�DAE = x + y; 4) AE = 18; EC = 2x + 2y; EB = 20; m�DEC = 130°; m�ECB = 85° DC = 2x + 5y; AB = 30 x = _____; y = _______ x = ______; y = _______

5) DE = x + y; EC = 12; CK = 2x - y 6) m�1 = 42; m�2 = x2; m�CED = 13x KD = 3x - 2y x______ y ________ x = ______; m�2 = _______

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Pre-AP Geometry Worksheet 5.8

II. For #7 – 10, find the values of x and y to make each quadrilateral a parallelogram. Show work.

7) m�A = 42; m�D = 8x - 6 8) AE = 3x - 40; EC = x; DE = y2; EB = y + 30 m�C = 3y x_______; y_______ x_________ y __________ 9) m�1 = 9y; m�2 = 3x; m�3 = 4x + 1 10) m�3 = y2; m�4 = y + 56 m�4 = 7y - 2 x______ y_________ y = _______ 11) Given: Parallelogram ABCD 12) Given: Parallelogram ABCE x__________; y__________ CD ___________; DE _________ 13) The measures of the angles of a hexagon are in the ratio of 4:5:5:8:9:9. Find the measure of each angle.

A B

CD

12

34

PRACTICE and APPLICATION EXERCISESON

LINE

HOM E W O R

K

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1. Given: AB ≅ CD, DE ≅ FC, EA ≅ BF 2. Given: ∠M ≅ ∠P, ∠MNQ ≅ ∠PQN,

Prove: ABCD is a parallelogram. ∠MQN ≅ ∠PNQ

Prove: MNPQ is a parallelogram.

NM

Q P

3. Given: M is the midpoint of HK and JL. 4. Given: ∠A and ∠C are right angles,

Prove: HJKL is a parallelogram. AD ≅ CB

Prove: ABCD is a parallelogram.

B

C

D

A

Analyze Mathematical Relationships (1)(F) For what values of x and y must ABCD be a parallelogram?

5. B

A D

C3x !

3y !

(y " 78)!

(4x # 21)!

6. 7.

8. 9.

3x ! 6 y ! 4

A B

CD

2y ! 2

3y " 9

10.

11. Display Mathematical Ideas (1)(G) Sketch two noncongruent parallelograms ABCD and EFGH so that AB ≅ EF and BC ≅ FG.

Can you prove that the quadrilateral is a parallelogram based on the given information? Explain.

12. 13. 14.

Proof Proof

A B

CD

FE

Proof Proof

L

H JM

K

BA

D C

y ! 1

2x

42y ! 7

BA

D C5x ! 8

2x " 7

D

A B

C

(3x ! 10)"

5y"

(8x ! 5)" (4x ! 33)"

A

B C

D

(2x # 15)"

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TEXAS Test Practice

18. Which piece of additional information would allow you to prove that PQRS is a parallelogram?

A. PQ ≅ RS C. ∠PTQ ≅ ∠RTS

B. QR ≅ SP D. ∠QPR ≅ ∠SRP

19. In quadrilateral ABCD, m∠A = 3x + 2, m∠B = x - 22, and m∠C = 2x + 52. Which value of x allows you to conclude that ABCD is a parallelogram?

F. 50 H. 28

G. 34 J. -12

20. Quadrilateral JKLM is a parallelogram. Which of the following does NOT guarantee that JNPM is a parallelogram?

A. N is the midpoint of JK and P is the midpoint of ML.

B. JM ≅ NP

C. JM } NP

D. ∠JMP ≅ ∠NPL

21. Write a proof using the diagram.

Given: △NRJ ≅ △CPT, JN } CT

Prove: JNTC is a parallelogram.

QP

S R

T

N

P

K

L

J

M

N

JR

P

C

T

15. Apply Mathematics (1)(A) Quadrilaterals are formed on the side of this fishing tackle box by the adjustable shelves and connecting pieces. Explain why the shelves are always parallel to each other no matter what their position is.

16. Justify Mathematical 17. Prove Theorem 6-9. Arguments (1)(G) Prove Given: ∠A is supplementary to ∠B.

Theorem 6-12. ∠A is supplementary to ∠D. Given: BC } DA, BC ≅ DA Prove: ABCD is a parallelogram. Prove: ABCD is a parallelogram.

A B

CD

Proof Proof

A

B C

D

B

A D

C

268 Lesson 6-3 Proving That a Quadrilateral Is a Parallelogram

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