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)