Download Geometry 1-6 9-2

Five-Minute Check (over Lesson 1–5)
CCSS
Then/Now
New Vocabulary
Key Concepts: Polygons
Example 1: Name and Classify Polygons
Key Concepts: Perimeter, Circumference, and Area
Example 2: Find Perimeter and Area
Example 3: Standardized Test Example: Largest Area
Example 4: Perimeter and Area on the Coordinate Plane
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Over Lesson 1–5
Refer to the figure. Name
two acute vertical angles.
Refer to the figure. Name a
linear pair whose vertex is E.
Refer to the figure. Name an
angle supplementary to ∠BEC.
∠1 and ∠2 are a pair of supplementary angles, and
the measure of ∠1 is twice the measure of ∠2. Find
the measures of both angles.
If RS is perpendicular to ST and SV is the angle
bisector of ∠RST, what is m∠TSV?
Over Lesson 1–5
Refer to the figure. Name
two acute vertical angles.
A. ∠AED and ∠BEC
B. ∠AEB and ∠DEC
C. ∠DEA and ∠DEC
D. ∠BEC and ∠BEA
2
Over Lesson 1–5
Refer to the figure. Name
two acute vertical angles.
A. ∠AED and ∠BEC
B. ∠AEB and ∠DEC
C. ∠DEA and ∠DEC
D. ∠BEC and ∠BEA
Over Lesson 1–5
Refer to the figure. Name a
linear pair whose vertex is E.
A. ∠AED, ∠BEC
B. ∠AEB, ∠BEA
C. ∠CED, ∠AEB
D. ∠AEB, ∠AED
3
Over Lesson 1–5
Refer to the figure. Name an
angle supplementary to ∠BEC.
A. ∠AEB
B. ∠AED
C. ∠AEC
D. ∠CEB
Over Lesson 1–5
∠1 and ∠2 are a pair of supplementary angles, and
the measure of ∠1 is twice the measure of ∠2. Find
the measures of both angles.
A. m∠
∠1 = 60, m∠
∠2 = 120
B. m∠
∠1 = 100, m∠
∠2 = 80
C. m∠
∠1 = 100, m∠
∠2 = 50
D. m∠
∠1 = 120, m∠
∠2 = 60
4
Over Lesson 1–5
If RS is perpendicular to ST and SV is the angle
bisector of ∠RST, what is m∠TSV?
A. 30
B. 45
C. 55
D. 60
Content Standards
G.GPE.7 Use coordinates to compute
perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance
formula.
Mathematical Practices
2 Reason abstractly and quantitatively.
6 Attend to precision.
5
You measured one-dimensional figures.
• Identify and name polygons.
• Find perimeter, circumference, and area of
two-dimensional figures.
• polygon
• equiangular polygon
• vertex of a
polygon
• regular polygon
• concave
• convex
• perimeter
• circumference
• area
• n-gon
• equilateral
polygon
6
Name and Classify Polygons
A. Name the polygon by its number of sides. Then
classify it as convex or concave and regular or
irregular.
There are 4 sides, so this is a quadrilateral.
No line containing any of the sides will pass through the
interior of the quadrilateral, so it is convex.
The sides are not congruent, so it is irregular.
Answer: quadrilateral, convex, irregular
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Name and Classify Polygons
B. Name the polygon by its number of sides. Then
classify it as convex or concave and regular or
irregular.
There are 9 sides, so this is a nonagon.
Lines containing some of the sides will pass through the
interior of the nonagon, so it is concave.
Since the polygon is concave, it must be irregular.
Answer: nonagon, concave, irregular
A. Name the polygon by the
number of sides. Then classify it
as convex or concave and
regular or irregular.
A. triangle, concave, regular
B. triangle, convex, irregular
C. quadrilateral, convex,
regular
D. triangle, convex, regular
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B. Name the polygon by the
number of sides. Then classify it
as convex or concave and
regular or irregular.
A. quadrilateral, convex,
irregular
B. pentagon, convex,
irregular
C. quadrilateral, convex,
regular
D. quadrilateral, concave,
irregular
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Find Perimeter and Area
A. Find the perimeter and area of the figure.
P = 2ℓ + 2w
= 2(4.6) + 2(2.3)
A = ℓw
= (4.6)(2.3)
= 13.8
= 10.58
Answer: The perimeter of the rectangle is 13.8 cm.
The area of the rectangle is 10.58 cm2.
Find Perimeter and Area
B. Find the circumference and area of the figure.
= = (4) = 8π
π
= 16
Answer: The circumference of the circle is 8π inches
The area of the circle is 16π square inches.
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A. Find the perimeter and
area of the figure.
A. P = 12.4 cm, A = 24.8 cm2
B. P = 24.8 cm, A = 34.83 cm2
C. P = 34.83 cm, A = 69.66 cm2
D. P = 24.4 cm, A = 32.3 cm2
B. Find the circumference and area
of the figure.
A. C = 50.3 m, A = 25.1 m2
B. C = 50.3 m, A = 201.1 m2
C. C = 16π m, A = 64π m2
D. C = 64π m, A = 16π m2
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Largest Area
Terri has 19 feet of tape to mark an area in the
classroom where the students may read. Which of
these shapes has a perimeter or circumference that
would use most or all of the tape?
A square with side length of 5 feet
B circle with the radius of 3 feet
C right triangle with each leg length of 6 feet
D rectangle with a length of 8 feet and a width of 3 feet
Read the Test Item
You are asked to compare the perimeters or
circumference of four different shapes.
Largest Area
Find each perimeter or circumference.
Square
Right Triangle
c2 = a 2 + b 2
P = 4s s = 5
2
= 4(5)
= 20 feet
Circle
C = 2π
πr
r=3
= 2π
π(3)
= 6π
π
≈ 18.85 feet a=b=6
2
= 6 + 6 = 72
=6 2
P =a+b+c
=6+6+6 2
≈ 20.49 feet
Rectangle
P = 2ℓ + 2w
= 2(8) + 2(3)
ℓ = 8, w = 3
The only shape for which Terri = 22 feet
has enough tape is the circle.
12
Each of the following shapes has a perimeter of
about 88 inches. Which one has the greatest area?
A. a rectangle with a length
of 26 inches and a width
of 18 inches
B. a square with side length
of 22 inches
C. a right triangle with each
leg length of 26 inches
D. a circle with radius of
14 inches
Perimeter and Area on the Coordinate Plane
Find the perimeter (to the nearest unit) and area of
a pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4),
D(–3, –4), and E(–3, 1).
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Perimeter and Area on the Coordinate Plane
Step 1
Notice CD = 6 and DE = 5
To find AB, BC and EA
use = Δ + Δ = 4
+ 4
= 16 + 16 = 32
= 4 2
= 1
+ 4
= 3
+ 3
= 1 + 16 = 17
= 9 + 9 = 18
= 17
= 3 2
Perimeter and Area on the Coordinate Plane
Step 1
So
= 4 2
= 17
= 6
= 5
= 3 2
And the perimeter of pentagon ABCDE
is 7 2 + 17 + 6 + 5 units (or about 25 units).
Note that 4 2 + 3 2 = 7 2
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Perimeter and Area on the Coordinate Plane
Step 2 Divide the pentagon into two
triangles and a rectangle.
Find the area of the triangles.
Area of Triangle 1
Find the area of the rectangle.
1
= 6 3 = 9
2
Area of Triangle 2
5
1
= 5 1 =
2
2
A = (5)(6) = 30
The area of pentagon ABCDE is
9 + 2.5 + 30 or 41.5 square units.
Answer: The perimeter is about 25
units and the area is 41.5 square
units.
Find the perimeter of
quadrilateral WXYZ with
W(2, 4), X(–3, 3), Y(–1, 0),
and Z(3, –1).
A.
+ + B. 17.93
C.
D. !
"
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