Date
Mon.
01/02/2017
Tuesday
01/3/17
Wednesday
01/4/17
Thursday
01/5/17
Friday
01/6/17
Monday
01/9/17
Tuesday
01/10/17
Wednesday
01/11/17
Thursday
01/12/17
Friday
01/13/17
Mon.
01/16/17
Tuesday
01/17/17
Wednesday
01/18/17
Thursday
01/9/17
Friday
01/20/17
GT/Honors Geometry
Jan 3 –Jan 20,2017 – Quadrilateral and areas of 2-D
Topic
Assignment
No School – Professional Development
Teachers work day
6.1 Revisit polygon angle sum theorem. Interior
and Exterior angles of regular polygons.
Pg. 253: #1-9, 11-14, 16,
18-19.
6.2 Students will explore the properties of
parallelograms.
WS 6.2:#1-11, Pg 259: 11,17-21
6.3 Students will Prove a quadrilateral is a
parallelogram in a variety of ways.
WS 6.3: #1-30, Pg 267: 12-14, 16-17
6.4 Students will explore the properties of special
parallelograms to solve algebraic problems, i.e,
Rhombus, Rectangles, Squares.
Quiz 1 Parallelograms
WS 6.4: #1-32, Pg 273: 13, 17-22
6.4 and 6.5 - Rhombus, Rectangles, Squares.
6.4, 6.5 (cont’d) Rhombus, Rectangles, Squares.
6.6 Students will explore properties of trapezoids,
isosceles trapezoids, and mid segment of a
trapezoid.
Students will explore how quadrilaterals are
formed by connecting midpoints.
7.1 Students will explore quadrilaterals in
coordinate plane.
Pg. 279: #1-8, 10-16, 21-23, 25-28.
Pg. 279: #1-8, 10-16, 21-23, 25-28.
WS 6.6: #1-14.
WS: #1-14
pgs. 299 -300 #1-3, 7-9, 13-16, 30-31
MLK – No School
7.1 Students will explore quadrilaterals in
coordinate plane.
7.2 Students will explore quadrilaterals in
coordinate plane – Do problems 1, 2, 3 from
Text book pp. 303-304 and WS
Test Review: 6.1 to 7.2
Pg. 300: # 18-26, 30
Pg. 304: #1-7, 12, 17-20
Pg. 288: #1-37. Pg 315: #11-20.
Test quadrilaterals
1
6-2 Notes: Properties of Parallelograms
Any four-sided polygon is called a quadrilateral. A segment joining any two nonconsecutive
vertices is called a diagonal. A special kind of quadrilateral in which both pairs of opposite sides
are parallel is called a parallelogram (this is the definition of a parallelogram).
You can use what you know about parallel lines and transversals to prove some theorems about
parallelograms.
Def. Parallelogram  Opposite sides are parallel
 Parallelogram → Opposite sides are 
→ Opposite angles are 
Parallelogram → Diagonals bisect each other
Parallelogram → Consecutive angles are supplementary
 Parallelogram


If each quadrilateral is a parallelogram, find the values of x, y, and z.
Y°
1.
105°
x°
2.
78°
z°
44°
x°
31°
Y°
3.
z°
z°
73°
x°
Y°
29°
4. In parallelogram ABCD, mA = 3x and
mB = 4x + 40. Find the measure of angles
A, B, C, and D.
5. In parallelogram RSTV, diagonals RT and
VS intersect at Q. If RQ = 5x + 1 and
QT = 3x + 15, find QT.
Explain why it is impossible for each figure to be a parallelogram.
10
6.
8
8
7.
130°
50°
55°
125°
11
2
A
Find x and y so that ABCD is a parallelogram.
B
8. AB = 3x + 2y; BC = 3; CD = 7; DA = 2x + y
D
C
A
B
9. mA = 2x + 8y; mC = 4x + 3y + 54; mD = x + 2y + 16
D
10. Find x so that ABCD is a parallelogram: AB = x2 - 3; CD = 2x + 12
C
A
D
B
C
11. PQRT has vertices P(-4, 7), Q(3, 0), R(2, -5), and T(-5, 2). Determine if PQRT is a
parallelogram.
3
6-3 Notes: Proving that a Quadrilateral is a Parallelogram
You can show that a quadrilateral is a parallelogram if you can show that one of the following is true.
Def: Both pairs opp. Sides




 Parallelogram
Both pairs of opp. Sides  → Parallelogram
Diagonals bisect each other → Parallelogram
Both pairs opp. Angles  → Parallelogram
One pair of opp. Sides are both and  → Parallelogram
Determine if each quadrilateral is a parallelogram. Justify your answer.
1.
40°
2.
30°
30°
3.
110°
40°
70°
Determine whether quadrilateral ABCD with the given vertices is a parallelogram. Explain.
4. A(2,5), B(5,9), C(6,3), D(3,-1)
5. A(-1,6), B(2,-3), C(5,0), D(2,9)
4
Geometry
Worksheet – 6.3 Parallelograms
Name____________________________________
Date______________________Period_________
Are the following parallelograms? If yes, why? (use one of the five reasons from section 6.3) If no, tell what
else would be needed.
1. _______________________
_______________________
2. _______________________
_______________________
3. _______________________
_______________________
7
5
3
3
7
7
5
7
4. _______________________
_______________________
5. _______________________
_______________________
8
100˚
70˚
120˚
6. _______________________
_______________________
110˚
60˚
80˚
8
7. _______________________
_______________________
8. _______________________
_______________________
9. _______________________
_______________________
17
30˚
30˚
17
10. _______________________
_______________________
110˚
11. _______________________
_______________________
70˚
M is the midpoint of AC and BD
9
A
M
110˚
13. ______________________
_______________________
B
5
5
70˚
12. ______________________
_______________________
9
14. ______________________
_______________________
50˚
50˚
D
C
15. ______________________
_______________________
130˚
19
25˚
25˚
19
5
State whether the given information is sufficient to support the statement, “Quadrilateral ABCD is a
parallelogram.” If the information is sufficient, state the reason.
A
2
D
4
1
O
B
16. AB  CD and AB CD
17. AO = OC and BO = OD
18. AB CD and BC AD
3
C
19. AC  BD and AO = OC
20. 1  4 and AB  DC
21. 1  4 and AD BC
22. AB  CD and BC  AD
23. 1  4 and 2  3
24. AB  CD and BC AD
25. BC  AD and BC AD
26. 2  3 and AB CD
27. 2  3 and BC  AD
28. 2  3 and AB  CD
29. BAD  BCD and ABC  ADC
30. BAD is supplementary to ADC
ADC is supplementary to BCD
6
Geometry Worksheet
6.4 Rectangles, Squares & Rhombi
Name_____________________________
Date_________________Period________
1. In rectangle ABCD, AB = 2x + 3y, BC = 5x – 2y, CD = 22, and AD = 17. Find x and y.
A
B
E
D
In the diagram for problems 2-7,QRST is a rectangle and QZRC is a parallelogram.
2. If QC = 2x + 1 and TC = 3x – 1,
find x.
C
3. If mTQC = 70, find mQZR.
Z
Q
R
Q
S
T
Z
R
C
C
T
4. If mRCS = 35, find mRTS.
S
5. If mQRT = mTRS, find mTCQ. Z
Z
Q
Q
R
R
C
C
T
T
S
6. If RT = x2 and QC = 4x – 6, what is the value of
x?
Z
Q
S
7. RZ = 6x, ZQ = 3x + 2y, and CS = 14 – x. Find the
values of x and y. Is QZRC a “special”
parallelogram? If so, what kind?
Z
R
C
Q
R
C
T
S
T
S
Use rectangle STUV for questions 8-11.
S
8. If m1 = 30, m2 = _______
6
7
K
1
8
9. If m6 = 57, m4 = _______
10. If m8 = 133, m2 = _______
V
11. If m5 = 16, m3 = _______
5
4
3
T
U
13. ABCD is a square. If mDBC = x2 – 4x, find x.
B
A
C
12. ABCD is a rhombus. If the perimeter of
B
ABCD = 68 and BD = 16, find AC.
A
2
D
D
C
7
Use rhombus ABCD for problems 14-19
B
A
14. If mBAF = 28, mACD = ______.
15. If mAFB = 16x + 6, x = _______.
F
16. If mACD = 34, mABC = _______.
D
17. If mBFC = 120 – 4x, x = ______.
C
18. If mBAC = 4x + 6 and mACD = 12x – 18, x = ______.
19. If mDCB = x2 – 6 and mDAC = 5x + 9, x = ______
20. ABCD is a square. AB = 5x + 2y, 21. A contractor is measuring for the foundation of a building that
AD = 3x – y, and BC = 11.
is to be 85 ft by 40 ft. Stakes and string are placed as shown.
Find x and y.
B The outside corners of the building will be at the points where the
A
strings cross. He then measures and finds WY = 93 ft and XZ = 94
ft. Is WXYZ a rectangle? If not, which way should stakes E and F
be moved to made WXYZ a rectangle?
D
C
85 ft
F
G
H
W
X
Z
Y
D
40 ft
C
B
A
22. ABCD is a rectangle. Find the length of each
diagonal if AC = 2(x – 3) and BD = x + 5.
E
23. ABCD is a rectangle. Find each diagonal if
3c
and BD = 4 – c.
AC 
9
Given rectangle QRST
________24. If RX  QT , find mTXS.
Q
R
X
________25. If mRQS = 30° and QS = 13, find SR.
________26. If mQST = 45° and QT = 6.2, find QR.
T
S
8
28. Given square PQRS, SR = x2 – 2x, QR = 4x – 5.
Find x, SR, and QR.
27. Given rhombus ABCD, AB = 5x + y – 1, BC = 18,
CD = 8x – 2y + 2. Find x and y.
P
C
B
T
E
A
Q
S
D
R
Determine whether WXYZ is a parallelogram, a rectangle, a rhombus, or a square for each set of vertices. State
yes or no for each and explain why or why not. Show work to support the explanations. For example, if you say the
sides are parallel then you need to calculate the slopes.
29. W(5, 6), X(7, 5), Y(9, 9), Z(7, 10)
Parallelogram:
Rectangle:
Rhombus:
Square:
30. W(-3, -3), X(1, -6), Y(5, -3), Z(1, 0)
Parallelogram:
Rectangle:
Rhombus:
Square:
Determine whether EFGH is a parallelogram, a rectangle, a rhombus, or a square for each set of vertices. State
yes or no for each and explain why or why not. Show work to support the explanations. For example, if you say the
sides are parallel then you need to calculate the slopes.
31. E(0, -3), F(-3, 0), G(0, 3), H(3, 0)
Parallelogram:
Rectangle:
Rhombus:
Square:
32. E(2, 1), F(3, 4), G(7, 2), H(6, -1)
Parallelogram:
Rectangle:
Rhombus:
Square:
9
Geometry Worksheet
Trapezoids (6.6)
Name_________________________________
Date____________________Period_________
A
1. Given: Isosceles trapezoid ABCD, mBAC = 30 and mDBC = 85
m1=_______
m5=_______
m ADC =_______
m2=_______
m6=_______
m BCD =_______
m3=_______
m7=_______
m DAB =_______
m4 =_______
m8 =_______
mCBA=_______
7
8
5
D
B
A
6
3
1
2
4
C
2. Given: Isosceles trapezoid JXVI, mJVI = 42 and mIJV = 65
m1=_______
m2=_______
m6=_______
m7=_______
J
m11=_______
2
1
5
m12=_______
m3=_______
m8=_______
m JIV =_______
m4=_______
m9=_______
mIJX=__________
m5 =________
m10=_______
I
6
8
9
7
3
4
X
10A
12
11
V
3. Given: Isosceles trapezoid JXVI, mIXV = 83 and mVJX = 28
m1=_______
m6=_______
J
m11=_______
m2=_______
m7=_______
m12=_______
m3=_______
m8=_______
m IVX =_______
m4=_______
m9=_______
mVXJ=__________
m5 =________
m10=_______
2
I
3
4
1
5
6
8
9
7
X
10A
11
12
V
10
4. VW is the median of a trapezoid that has bases MN and PO , with V on OM and W on PN . If the vertices
of the trapezoid are M(2, 6), N(4, 6), P(10, 0), and O(0, 0), find the coordinates of V and W.
5. VW is the median of a trapezoid MNPO that has bases MN and PO , with V on PM and W on ON . If M(5,
10), N(9, 10), V(3, 7), and W(11, 7), find the coordinates of P and O.
XY is the median of trapezoid QRST in problems 6-11.
6. XY=18 and TS = 7.
7. TS = n and QR = 6.
Find QR.
Find XY in terms of n.
R
Q
T
9. TX = ½ (SR) and mT=130.
Find mR.
X
T
10. ST = a and QR = 2b.
Find XY.
Q
X
Y
T
R
S
Y
S
Q
X
Y
S
T
Q
T
X
S
11. QX=SY and mTXY = 45.
Find mR.
R
R
Q
Y
S
S
X
R
Y
Y
Q
8. XY=16. Find TS+QR.
R
X
T
In problems 12-14, trapezoid ABCD is isosceles. Find the variable in each.
12. AB = x+5 and CD = 3x + 3
13. m  ABC=3x–7 and m  ADC=5x+3
14. AC = x2 + 6 and BD = 8x – 9.
C
B
A
D
C
B
A
D
C
B
A
D
11
NOTE: Quadrilaterals from Midpoints
A
E
B
I. Given: Quadrilateral ABCD
E, F, G, and H are the midpoints of
AB , BC , CD , and DA respectively.
F
H
1. Does EFGH “look” like a special kind of quadrilateral?
C
G
D
2. Draw diagonal AC . ∆_______ and ∆_______ are formed.
How is EF related to AC ?
_____________________________________________________
3. How is HG related to AC ?_________________________________
4. What kind of quadrilateral is EFGH?________________________
5. Why?________________________________________________
E
A
II. Quadrilateral ABCD is a rhombus. Again E, F, G, and H are midpoints.
6. What kind of angle is  EHG?________________
B
F
H
D
7. What kind of quadrilateral is EFGH?____________________
G
C
III. Quadrilateral ABCD is a rectangle. Again, E, F, G, and H are midpoints.
8. How are HE and EF related?
_______________________________________
(Hint: How are AC and BD related?)
A
E
B
F
H
9. What kind of quadrilateral is EFGH?
________________________________
D
G
C
12
IV. ABCD is a quadrilateral where E, F, G, and H are midpoints.
11. If quadrilateral ABCD is a square, then quadrilateral EFGH is a
______________
12. If quadrilateral ABCD is a trapezoid, then quadrilateral EFGH is a
_______________
13. If quadrilateral ABCD is an isosceles trapezoid, then quadrilateral EFGH
is a __________________.
14. Given: ISOE is an isosceles trapezoid
T, R, A, and P are midpoints
IO = 14
m  RIT = 70˚
m  SRA = 45˚
Find:
m  1 = ________
m  9 = ________
m  2 = ________
m  10 = ________
m  3 = ________
m  11 = ________
m  4 = ________
m  12 = ________
m  5 = ________
m  13 = ________
m  6 = ________
m  14 = ________
m  7 = ________
m  15 = ________
m  8 = ________
m  16 = ________
SE = ________
RA = ________
S
R
I
13
1
2
A
3
4
16
14
5
O
6
15
7
12
11
T
10
8
P
9
E
13
Consecutive sides are _______________.
Opposite sides are ___________________.
Consecutive angles are
__________________.
Defined by:
Four ___________ and four _____________
Diagonals will ____________________.
Angles always add up to ____________.
Angles:
Sides:
Defined by:
_______________ sides are _____________
and
Diagonals:
_______________.
Area:
All parallelograms are ______________.
Rectangles
Angles:
Sides:
Defined by:
A rectangle is a ________________ where all
four
Diagonals:
angles measure ______.
Area:
All rectangles are _____________;
____________
14
Rhombi (Rhombus)
Angles:
Sides:
Defined by:
A rhombus is a ______________ where
_______
_______ sides are equal.
Diagonals:
All rhombi are _________________.
Area:
Squares
Angles:
Sides:
Defined by:
A square is a ________________ where all
four
sides are _______________, and all four
angles are _____.
Diagonals:
Area:
All squares are _____________;
____________ ; _____________
Trapezoids
Angles:
Sides:
Defined by:
A trapezoid is a ______________ where two
opposite sides are ____________ and the
remaining opposite sides are _____
_______________.
Isosceles trapezoids have legs that are
____________.
Diagonals:
Area:
15
Geometry – GT/PreAP
Unit Review – Quadrilaterals
Find each of the following values.
Use parallelogram GRAM for problems 1-4.
Name_______________________________________
Date__________________________Period_________
R
_______1. GA = 3x – 10 and GP = x + 20. Find x.
A
P
G
_______2. m  GMR = 37˚ and m  AMG = 95˚, find
m  GRM.
23
M
37
________3. m  RGM = 75˚, find m  GMA.
x = ______ 4. RA = 2x + y, GR = 3x – y, find x and y.
y = ______
Use rectangle RECT for problems 5-8.
_________5. If TA = 3x – 7 and AC = 2x + 2, find x.
R
8
2
1
9
7
T
_________6. If m  2 = 33˚, find m  11.
6
A
10
E
3
11
5
4
C
_________7. If RT = 2x + 5 and EC = 4x – 11, find x.
________8. If m  1 = x2 – 4 and m  8 = x + 52, find x.
Use rhombus RHOM for problems 9-11.
16
M
x=_________ 9. If MO = 24, MR = 4x + 2y + 2, and RH = 5x – y + 14, find x and y.
1
y=_________
3
2
R
4
T
8
O
_________10. If RO = 24 and MH = 10, find MR.
7
5
6
H
__________11. If m  7 = 39˚, find m  2.
Use square SQUA for problems 12-14.
S
__________12. If AU = x2 + 2 and SA = 5x – 4, find x.
Q
R
A
__________13. If m  ARS = 6x, find x.
U
_________14. If m  QAU = 3x – 12, find x.
Use trapezoid TUVW with median XY for problems 15-17.
T
U
104˚
________15. m  V
Z
________16. TU = 15, WV = 33, find ZY.
W
54˚
Y
V
________17. TU = x – 12, ZY = x + 15, and WV = 3x – 8. Find x.
17
Use isosceles trapezoid TRAP for problems 18-20.
_______18. Find m  1.
T
79˚
32˚
7
_______19. Find m  7.
8
_______20. Find m  3.
P
6
9
5
R
4
10
1
2
3
A
In problems 21-23, if there is enough information to state that the quadrilateral is a parallelogram give the reason.
Write none if there is not enough information to state that the quadrilateral is a parallelogram.
21. E is the midpoint of AC and BD .
A
1
22. 2  6 and 3  7
8
D
7
3
2
E
6
B
4
5
C
23. 8  4 and AD  BC
24. The coordinates of the vertices of quadrilateral ABCD are A(-4, -2), B(-1, 3), C(4, 0), and D(1, -5). Determine
whether ABCD is a parallelogram, a rectangle, a rhombus, or a square. State yes or no for each and explain
why or why not. Show work to support the explanations. For example, if you say the sides are parallel then
you need to calculate the slopes.
Parallelogram:
Rectangle:
Rhombus:
Square:
25. The coordinates of the vertices of quadrilateral PQRS are P(4, 4), Q(1, 2), R(2, -2), and S(5, 0). Determine
whether PQRS is a parallelogram, a rectangle, a rhombus, or a square. State yes or no for each and explain
why or why not. Show work to support the explanations. For example, if you say the sides are parallel then
you need to calculate the slopes.
Parallelogram:
Rectangle:
Rhombus:
Square:
26. The coordinates of the vertices of quadrilateral WXYZ are W(5, 0), X(6, -8), Y(-1, -4), and Z(-2, 4).
Determine whether WXYZ is a parallelogram, a rectangle, a rhombus, or a square. State yes or no for each
and explain why or why not. Show work to support the explanations. For example, if you say the sides are
parallel then you need to calculate the slopes.
Parallelogram:
Rectangle:
Rhombus:
Square:
18
27. Find the coordinates of the 3 possible points for the missing vertex in a parallelogram if three of the vertices
are A(-2, -1, B(-1, 3), and C(4, 1)
28: skip
29. ∆ABC has midpoints D, E, and F. If the perimeter of
∆DEF is 23, then find the perimeter of ∆ABC.
E
A
D
B
F
C
30. skip
31. ISOE is an isosceles trapezoid. T, R, A, and P are midpoints.
IO = 12
m  RIT = 75˚
S
m  SRA = 40˚
1
A
O
Find: m  1 = ________
R
m  2 = ________
2
P
m  3 = ________
RA = ________
I
T
3
E
AP = ________
19
20