Name:
Period
GP
UNIT 11: QUADRILATERALS AND POLYGONS
I can define, identify and illustrate the following terms:
Quadrilateral
Parallelogram
Rhombus
Rectangle
Square
Trapezoid
Isosceles trapezoid
Kite
Concave polygon
Convex Polygon
Regular Polygon
Diagonal
Dates, assignments, and quizzes subject to change without advance notice.
Monday
Tuesday
16
MLK DAY
No School
6-1
6-2 & 6-3
Polygons
Parallelograms
24
23
6-4 & 6-5
6-6
Special Parallelograms
Trapezoids & Kites
31
30
Block Day
18/19
17
Quadrilateral
Proofs
Review
25/26
Quadrilaterals on the
Coordinate Plane
1/2
Friday
20
6-3
Parallelograms
27
QU I Z
3
TEST
Tuesday, 1/17/12
6-1: Properties and Attributes of Polygons
I can name polygons with up to ten sides.
I can classify a polygon as concave or convex and regular or irregular.
I can find the measure of an interior angle of any regular polygon.
I can find the measure of an exterior angle of any regular polygon.
PRACTICE: Polygon Discovery Questions
Wednesday, 1/18/12 or Thursday, 1/19/12
6-2 & 6-3: Properties of Parallelograms
I know and can use the properties of a parallelogram to solve problems.
PRACTICE: pp. 395-396 #21-24, 28-30, 32-43, 46, 47 and p 402 # 9-13, 20-23
Friday, 1/20/12
6-3: Properties of Parallelograms
I know and can use the properties of a parallelogram to solve problems.
PRACTICE: p 402 # 14-15, 36-37,39
Monday, 1/23/12
6-4 & 6-5: Properties of Special Parallelograms
I know and can use the properties of a rhombus to solve problems.
I know and can use the properties of a rectangle to solve problems.
I know and can use the properties of a square to solve problems.
PRACTICE: pp. 412-415, #18-31, 41, 47; p. 422 #11-16, 24-26
Tuesday, 1/24/12
6-6: Properties of Kites and Trapezoids
I know and can use the properties of a trapezoid to solve problems.
I know and can use the properties of an isosceles trapezoid to solve problems.
I know and can use the properties of a kite to solve problems.
PRACTICE: pp. 433-434 #19-25, 27, 30, 32, 34-35, 38 proof (use picture below)
Wednesday, 1/25/12 or Thursday, 1/26/12
Quadrilaterals in the Coordinate Plane
I can use the find the slope and distance between two points.
I can use the properties of quadrilaterals to prove that a figure in the coordinate plane is a
parallelogram, rhombus, rectangle, square, or trapezoid.
PRACTICE: Quadrilaterals in the Coordinate Plane Worksheet
Friday, 1/27/12
QUIZ: Properties of Quadrilaterals
PRACTICE: Begin Review p 438 #1-67
Monday, 1/30/12
Quadrilateral Proofs
I can write a two-column proof using properties of quadrilaterals.
I can use the properties of quadrilaterals to draw conclusions about their relationships.
PRACTICE: Quadrilateral Proofs Worksheet
Tuesday, 1/31/12
Review
I can use properties and attributes of polygons and quadrilaterals to solve problems and write proofs.
PRACTICE: Pg 438 – 441, #5-28, 33-47, 53-67
All answers are in the back of the book.
Wednesday, 2/1/12 or Thursday, 2/2/12
Test 10: Quadrilaterals and Polygons
Name:
Period:
GH
Quadrilaterals in the Coordinate Plane
1 – 2: Show that the quadrilateral with the given vertices is a parallelogram.
1. A(–3, 2), B(–2, 7), C(2, 4), and D(1, –1)
2. J(–1, 0), K(–3, 7), L(2, 6), and M(4, –1)
3. The vertices of square PQRS are P(–4, 0), Q(4, 3), R(7, –5), and S(–1, –8). Show that the diagonals
of square PQRS are congruent perpendicular bisectors of each other.
4 – 5: Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle,
rhombus, or square. Give all names that apply.
4. A(–10, 4), B(–2, 10), C(4, 2), and D(–4, –4)
5. J(–9, –7), K(–4, –2), L(3, –3), and M(–2, –8)
6 – 8: Give the best name for a quadrilateral with the given vertices.
6. (–4, –1), (–4, 6), (2, 6), (2, –4)
7. (–4, –3), (0, 3), (4, 3), (8, –3)
8. (–8, –4), (–5, 1), (1, –5), and (–2, –10)
9. Which of the following is the best name for
figure WXYZ with vertices W(–3, 1), X(1, 5),
Y(8, –2), and Z(4, –6)?
(a) Parallelogram
(c) Rhombus
10. Four lines are represented by the equations below:
l : y = −x +1
m : y = −x + 7
n : y = 2x +1
a. Graph the four lines in the coordinate plane.
b. Classify the quadrilateral formed by the lines.
c. Suppose the slopes of lines n and p change to 1.
Reclassify the quadrilateral.
(b) Rectangle
(d) Square
p : y = 2x + 7
Name:
Period:
GH
Quadrilateral Proofs
1. Given: PSTV is a parallelogram. PQ ≅ RQ
Prove: STV ≅ R
2. Given: ABCD and AFGH are parallelograms.
Prove: C ≅ G
Q
S
F
T
P
A
R
V
3. Given: EFGH is a rectangle.
J is the midpoint of EH .
Prove: FJG is isosceles.
F
G
D
H
4. Given: GHLM is a parallelogram. L ≅ JMG
Prove: GJM is isosceles
J
G
K
H
E
H
J
L
G
M
5. Given: RHMB is a rhombus with diagonal HB . 6. Given: QRST is a parallelogram. PR ≅ TV .
Prove: HMX ≅ HRX
Prove: PQR ≅VST
M
Q
H
T
V
X
B
P
R
7. Given: l m and 15 ≅ 7
Prove: The four lines form a parallelogram
a
l
1 2
4 3
15 14
16 13
8. Given: ABCD is a rhombus.
E, F, G, and H are the midpoints of the sides.
Prove: EFGH is a parallelogram.
b
m
S
R
E
5
8
10 9
11 12
B
F
6
7
A
C
H
G
D
9. Given: DEFG is a parallelogram
Prove: mDHG = mEDH + mFGH
10. Given: ABCD is a rectangle
Prove: EDC ≅ ECD
11. Given: GHIJ is a rhombus
Prove: 1 ≅ 3
12. Given: PQ SR, QU ⊥ SR, PT ⊥ SR
Prove: PQUT is a rectangle
13. Given: Parallelogram ABCD
Prove: ABC ≅CDA
14. Given: Parallelogram ABCD
Prove: ABE ≅CDE
B
B
C
C
E
A
A
D
15. Given: Rectangle ABCD
Prove: ABC ≅DCB
D
16. Given: Isosceles Trapezoid ABCD
Prove: ABC ≅DCB
B
C
A
D
A
B
D
C
Angles in Polygons - Exploration
Name of
polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n-gon
# of Sides
# of Diagonals
from a vertex
# of triangles
in polygon
Sum of
interior angles
Measure of one
interior angle
Measure of one
exterior angle
Sum of
exterior angles
Name:_______________________________
Period:______
GH
Angles in Polygons – Assignment
I. Fill in the chart.
Polygon
Sum of Interior ∠ ’s
Each Interior
∠
Each Exterior
quadrilateral
decagon
20-gon
pentagon
triangle
12-gon
18-gon
hexagon
nonagon
36-gon
octagon
heptagon
72-gon
II. Solve the following word problems.
1) If the sum of the interior angles is 1980°, what is the name of the polygon?
2) If each of the exterior angles is 15°, what is the name of the polygon?
3) If each on the interior angles is 108°, what is the name of the polygon?
4) If it is a decagon, what is the sum of the exterior angles?
5) If the sum of the interior angles is 3600°, what is the name of the polygon?
6) If each of the exterior angles is 24°, what is the name of the polygon?
7) If each of the interior angles is 135°, what is the name of the polygon?
8) If each of the exterior angles is 60°, what is the name of the polygon?
9) If each interior angle is 160°, what is the name of the polygon?
∠
Sum of Exterior
∠ ’s