Name: _____________________________________________________________________ Period: _____

Pre-AP Geometry Unit 12: Quadrilaterals

Fifth Six Weeks 2011-2012

All work must be shown to receive full credit. 0 25 50* 75 80* 100

Tuesday

February 21

Day 1: Parallelograms

Hw: #1-39

Holt 6.2

Wednesday

February 22

Day 2: Proving Quads are

Parallelograms

Hw: #1-20

Holt 6.3

Thursday

February 23

Day 3: Rectangles & Squares

Hw: #1-26

Holt 6.4 & 6.5

Friday

February 24

Monday

February 27

Day 4: Rhombus & Kite

Hw: #1-13

Holt 6.4 – 6.6

Tuesday

February 28

Day 5: Trapezoids

Hw: #1-14

Holt 6.6

Wednesday

February 29

Day 6: Medians &

Midsegments

Hw: #1-19

Holt 6.6

Thursday

March 1

Day 7: Proofs

Hw: #1-5

Friday

March 2

Monday

March 5 Day 8: Review

Tuesday

March 6

Test: Unit 12 -

Quadrilaterals (major grade

– 5th 6 weeks)

Retest Deadline: Friday, 03.09.12

**If you failed the test, you must complete the retest which can be found on www.mrslaz.weebly.com. It will also

be posted in class. You must show all of your work, and you will receive a 70 if you complete all of the questions

CORRECTLY with work shown.**

Parent-Signed Grade Sheets Due:

2/22, 2/29, 3/7

SuperSTAAR

Math Writing

Day 1: Parallelograms

Classify each statement as true or false.

1. Every quadrilateral is a parallelogram.

2. Every parallelogram is a quadrilateral.

3. If quadrilateral RSTW is a parallelogram, then .

4. If quadrilateral DEFG is a parallelogram, then // .

5. There exists a parallelogram with all sides congruent.

6. There exists a parallelogram ABCD such that m∠A = 70 and m∠C = 80.

7. There exists a parallelogram with all angles congruent.

8. is a diagonal of parallelogram WXYZ.

9. If is drawn in parallelogram ABCD, then ∆ABC≅∆CDA.

Exercises #10-15 refer to parallelogram RSTW. Complete each statement.

10. //_____ 14. ∆RST≅______

11. ≅_____ 15. _____

12. ≅_____

13. ∠WRS≅_____

Exercises #16-21 refer to parallelogram CDEF.

16. CE = 12, CX = _____

17. FX = 8, FD = _____

18. m∠CDE = 72, m∠EFC = _____

19. m∠1 + m∠2 = 106, m∠FCD = _____

20. m∠3 = 88, m∠2 = _____

21. m∠4 = 41, m∠1 = _____

In each parallelogram, find the indicated measure.

22. Find AD. 23. Find HI.

24. Find m∠R. 25. Find QZ. XZ + YW = 52

W

X

R

T

S

F

X

C

E

D

1 2

3 4

A 4x + 3

D

B

C

2x + 1

7x - 12

H

K

I

J 3x + 36

5x + 4

Q

T

R

S

4x + 8

6x + 12

X

Q

W

Y

Z

3a - 5 4a - 10

Use parallelogram ABCD to answer the following questions.

26. If AB = 12, what other side has a length of 12?

27. If m∠ADC = 29, what is m∠CBA?

28. Does AB + BC = AD + DC?

29. Are ∠DCB and ∠ABC supplementary?

30. If BD = 2x + 8, then XD = _______.

31. If the perimeter of parallelogram ABCD is 72 and BC = 6.5, then AB = _______.

32. Is point X the midpoint of both and ?

33. If AB = 4x – 5, DC = 2x + 15, and BC = 4, then the perimeter of parallelogram ABCD is _______.

34. If AC = 6x + 14 and XC = x + 15, then AX = _______.

35. If m∠DAB = 5x – 7 and m∠ABC = 4x + 7, then m∠DCB = _______.

Given parallelogram KLMN, answer the following questions.

36. If KL = x/2, MN = 2x – 9, KL = _______.

37. If m∠K = 31, m∠M = 2 - 1, x = _______.

38. If m∠L = x – 40, m∠N = , m∠L = _______.

39. DE = x + y

BE = 10

AE = x – y

CE = 8

Find x and y if ABCD is a parallelogram.

A

X

D

B

C

A

E

D

B

C

Day 2: Proving Quads are Parallelograms

State whether the information given about quadrilateral SMTP is sufficient to prove that it is a

parallelogram.

Find the values of x and y for which the figure must be a parallelogram.

Find the value of x. Then tell whether the figure must be a parallelogram. Explain your answer in a

complete sentence.

Decide whether the quadrilateral is a parallelogram. Explain your answer in a complete sentence.

Day 3: Rectangles & Squares

Given: ABCD is a rectangle. Name all the parts that make true statements.

1. ≅

2. AD =

3. m∠BEC =

4. ≅

5. ⊥

6. ∆ABD≅

7. ∆BEC≅

Answer True or False.

8.

9. bisects

10. bisects ∠BAD

11.

12.

13. WXYZ is a rectangle.

The perimeter of ∆XYZ = 24.

XY + YZ = 5x – 1

XZ = 13 – x

Find WY.

14. Rectangle ABCD has vertices A(3, 4) B(-1, 6) C(-5, -2) D(-1, -4)

Find:

a) the midpoint of

b) AB

c) AD

d) the slope of

e) the slope of

Given: ABCD is a square. Answer True or False.

15.

16. bisects

17. bisects ∠BAD

18.

19.

D

B

C

E

A A Problems #1-12

A B

C D

E

Problems #15-19

20. SQRE is a square. The diagonals of SQRE intersect at A. Find:

a) m∠RSQ

b) m∠EAR

c) EA = 5x – 3, RA = 4x + 6. Find EQ

21. WXYZ is a square.

WX = 1 – 10x

YZ = 14 + 3x

Find YW.

22. ABCD is a rectangle. F lies on BC . E lies on DC . mBAF = 29 and mDAE = 39. Find mFAE.

23. In rectangle ABCD, AB = 15 and BC = 6. Find the length of the diagonal.

24. In rectangle ABCD, diagonals AC and BD intersect at E. If AE = 2x – 6y, EC = 2x + 6, and BD = 16, find x & y.

25. In rectangle ABCD, mBAD = 2(mDAC) + 38˚. Find mBAC.

26. The figure shows two similar rectangles. What is the length of PQ ?

1

2

3

4 5

6

7

8 9

10

11 12

A

B

C

D

A

B

C

D

E F G

H

63°

Day 4: Rhombus & Kite

1. Given: ABCD is a rhombus.

m∠3 = 56

Find:

m∠1 m∠7

m∠2 m∠8

m∠3 m∠9

m∠4 m∠10

m∠5 m∠11

m∠6 m∠12

2. Given: BDEG is a rectangle. ABCD is a rhombus.

Find:

a) m∠DAB

b) m∠BCG

c) m∠GCF

d) m∠DEG

WXYZ is a rhombus. (#3-4)

3. m∠X = 24(10 – x), m∠Z = 6(x + 15), find m∠Y. 4. WX = 3x + 2, XY = 5x − 10, find YZ.

5. Answer always, sometimes, or never.

a. If a quadrilateral is a rhombus, then it is _______________ a square.

b. If a quadrilateral is a square, then it is ________________ a rectangle.

c. If a rectangle is a rhombus, then it is _________________ a square.

d. If a quadrilateral is a rhombus, then it is __________________ a regular polygon.

6. Answer true or false.

a. Every rectangle is a parallelogram. b. The diagonals of a rhombus are perpendicular.

c. Every rhombus is a regular polygon. d. If a rectangle is equilateral, then it is a square.

7. Find the measure of each numbered angle. 8. Find the perimeter of the kite.

40° 2

3 4 5 6 7 8 9 10

11 30°

x - 4

17 x + 3

9. The following ordered pairs represent the endpoints of one diagonal of a kite (they are not all from the same

kite).

Find the midpoint of the diagonal. Find the length of the diagonal with the given endpoints.

a. (6, 4); (12, 2) b. (4, 5); (3, 2)

Find the slopes of the diagonals with the given endpoints.

c. (1, 2); (1, 1) d. (2, 3); (2, 3)

KITE is a kite. (Probs. #10, 11)

10. If mKIE = 50 and mKEI = x + 5(x − 2), find x.

11. If m11 = 4x and m10 = x + 10, find m8.

12. ABCD is a rhombus with diagonals AC and DB intersecting at R. If mBRC = 2x2 + 40, find x.

13. ABCD is a rhombus with diagonals AC and DB intersecting at R. If mADB = 2x − 1, mARB = 6x, mACB = y,

find x and y.

11

K

T

E I

8

10

3 2

Day 5: Trapezoids

1. In the isosceles trapezoid, m A = 70.

Find the measures of the other angles.

2. In the isosceles trapezoid, m A = 5k.

Find the measures of the other angles in

terms of k.

Problems #1 and 2

3. Find the lengths of the legs of isosceles trapezoid ABCD if A(0, 0) B(5, 0) C(3, 3) and D (2, 3).

4. Given: Isosceles trapezoid ABCD

mBAC = 30, mDBC = 85

Find: m1 m6 mDAB

m2 m7 mCBA

m3 m8

m4 mADC

m5 mBCD

5. Given: Isosceles trapezoid JXVI

mJVI = 42, mIJV = 65

Find: m1 m6 m10

m2 mJIV m11

m3 m7 m12

m4 m8 mIJX

m5 m9

Find the value(s) of the variable(s) in each isosceles trapezoid. 6. 7. 8.

Each trapezoid is isosceles. Find the measure of each angle.

9. 10.

A I

S G

8 5

7 6

4 2

A B

C D 1

3

3

2 5

9

7

11 12

J X

V I 4

1 6

8

10

3x − 3

x − 1

(6x+20)°

(4x)°

Y°

7x 2x+5

77° 1 105°

Find the value of the variable in each isosceles trapezoid.

11. 10. 13.

TV = 2x − 1

US = x + 2

14. Given: Isosceles trapezoid JXVI

mIXV = 83, mVJX = 28

Find: m1 m6 m10

m2 mIVX m11

m3 m7 m12

m4 m8 mVXJ

m5 m9

Day 6: Medians & Midsegments

In exercises 1 - 5, points M and N are the midpoints of AB and BC.

1. AC = 12, MN = ___________ 2. MN = 7, AC = ____________

3. AC = k, MN = ____________ 4. MN = p, AC = ____________

5. MB = 8, MA = ____________

RS is the median of trapezoid ABCD.

6. If AB = 10 and DC = 8, RS = __________ 7. If RS = 7, then AB + DC = ___________

8. If BC = 12, CS = __________ 9. If m A = 80, mDRS = ___________

10. If AB = 6x + 2, RS = x + 1, and DC = 4x 2, find x.

11. If RS = 20 and DC = 14, then AB = ______________

12. If DC = 2x + 8, RS = 4x + 18 and AB = 10x + 20, find RS.

XY is the median of trapezoid MNRS. Find the measures.

13. RS = 13.7, MN = 6.1, XY = _________ 14. XY = 11.3, MN = 8.4, RS = _________

Trap MNRS is isosceles with median XY. Find the following.

15. NX = 10, find MS. 16. mN = 40, find mS.

17. mR = 55, find mMYX.

Points R and S are the midpoints of AB and BC.

18. If RS = 5.6, AC = _________

19. If AC = 3x + 1 and RS = x + 3, then RS = __________

3

2 5

9

7

11

12

J X

V I 4

1 6

8

10

45° 3x°

60° (3x+15)° T U

S V

A B

D C

R S

R S

YX

N M

A C

R S

B

A C

M N

B

Day 7: Proofs

1. Given: ABCD is a rectangle

ACBE is a parallelogram

Prove: DB EB

Statements Reasons

1. ABCD is a rectangle 1.

2. DB AC 2.

3. ACBE is a parallelogram 3.

4. AC EB 4.

5. DB EB 5.

2. Given: ABCD is a trapezoid with AB // CD

AP bisects DAB

Prove: APD is isosceles

Statements Reasons

1. ABCD is a trapezoid with AB // CD, 1.

AP bisects DAB

2. DPA PAB 2.

3. DAP PAB 3.

4. DPA DAP 4.

5. AD PD 5.

6. APD is isosceles 6.

3. Given: ABCD , FG bisects DB

Prove: DB bisects FG

Statements Reasons

1. ABCD, FG bisects DB 1.

2. CD // BA 2.

3. CDB ABD, DFE BGE 3.

4. BE DE 4.

5. BEG DEF 5.

6. FE GE 6.

7. DB bisects FG 7.

D P C

BA

C F D

AGB

E

4. Given: CTGD, CO DG, AG CT

Prove: ∆COD ∆GAT

Statements Reasons

1. CO DG, AG CT 1.

2. COD and TAG are right angles 2.

3. COD TAG 3.

4. CTGD 4.

5. DC GT 5.

6. D T 6.

7. ∆COD ∆GAT 7.

5. Given: Isosceles Trapezoid RSPT

Prove: ∆TPQ is isosceles

Statements Reasons

1. Isosceles Trapezoid RSPT 1.

2. R S 2.

3. RS // TP 3.

4. R PTQ, S TPQ 4.

5. PTQ TPQ 5.

6. TQ PQ 6.

7. TPQ is isosceles 7.

D O G

C A T

Q

T P

R S

Day 8: Review

1. Given: Parallelogram ABCD with m 2 = 32, m 6 = 22, and m 11 = 61.

Find:

m 1 m 7

m 3 m 8

m 4 m 9

m 5 m 10

2. Given: Rectangle RECT. m 2 = 49

Find:

m 1 m 8

m 3 m 9

m 4 m 10

m 5 m 11

m 6 m 12

m 7

3. Given: Rhombus ABCD. m 4 = 33.

Find:

m 1 m 8

m 2 m 9

m 3 m 10

m 5 m 11

m 6 m 12

m 7

4. Given: Square SQUA. Find:

m 1 m 7

m 2 m 8

m 3 m 9

m 4 m 10

m 5 m 11

m 6 m 12

5. Given: Kite KITE. m12 = 52, m9 = 41.

Find:

m 1 m 7

m 2 m 8

m 3 m 10

m 4 m 11

m 5

A B

CD

11

109

12 5

6

34

78

R E

CT

1 2 34

567

8

9 10 1112

D C

BA1

3

2

1145

6

78

9

10

12

S Q

UA

12 3

4

567

8

910

1112

3

2

5 9

7

11 12

K

T

E I 4

1

6

8 10

6. Put a checkmark in the “I Agree” column by the statements that you think are true. For any statement that is

false, change any of the italicized words that you need to in order to make it true.

I Agree Statement

1. The hypotenuse is the shortest side of a right triangle.

2. The diagonals of a kite are perpendicular.

3. The consecutive sides of a parallelogram are congruent.

4. The median of a trapezoid is found by adding the base lengths.

5. A square is sometimes a rhombus.

6. An isosceles trapezoid has diagonals that bisect each other.

7. The consecutive angles in a parallelogram are congruent to each other.

8. A rhombus has four congruent sides.

9. A rectangle is always a square.

10. A rhombus has congruent diagonals.

7. Use these words in the diagram.

Isosceles trapezoids

Kites

Parallelograms

Quadrilaterals

Rectangles

Rhombi

Squares

Trapezoids

8. An open area at a local high school is in the shape of a quadrilateral. Two sidewalks crisscross this open area

as diagonals of the quadrilateral. If the walkways cross at their midpoints and the walkways are equal in

length, what is the shape of the open area?

A) a parallelogram B) a rhombus C) a rectangle D) a trapezoid

(1)

(2) (3) (4)

(7)

(5) (6)

(8)