2D Geometry: Geometric Relationships, Perimeter & Circumference Chapter Questions
1.
What are some of the special relationships between angles?
2.
Explain what a polygon is and how to determine if it is regular.
3.
How can you classify quadrilaterals?
4.
What are perimeter and circumference and how are they relevant in daily life?
2D Geometry: Geometric Relationships, Perimeter & Circumference Chapter Problems
Special Pairs of Angles
Classwork
1. If two angles have the same measure are they congruent?
2. Angle 1 and Angle 2 are complementary. If ∠1 has a measure of 420 what would the measure of ∠2
be?
3. Determine the measure of the unknown angle A in the figure below.
4.
5.
6.
7.
What is the complement of 720?
If Angle 1 measures 480 and Angle 2 measures 420 are these angles complementary?
Angle R and S are supplementary. If Angle R measures 1150 what is the measure of Angle S?
What is the measure of Angle A?
8.
9.
10.
11.
What is the supplement of 720?
If Angle X measures 530 and Angle Y measures 1270 are these angles supplementary?
What is the complement of 680? Supplement?
Using what you know about vertical angles, find the measure of the missing angles. You must be
able to explain why.
12. Parallel lines m and n are cut by a transversal l. If the measure of angle 5 is 37o determine the
measures of the remaining angles. You must be able to explain why.
Homework
13. Angle M has a measure of 360 and Angle N has a measure of 240. Are these two angles congruent?
14. Angle r and Angle s are complementary. If ∠𝑠 has a measure of 260 what would be the measure of
∠𝑟?
15. Determine the measure of the unknown angle A in the figure below.
16.
17.
18.
19.
What is the complement of 90?
If Angle x measures 530 and Angle y measures 1270 are these angles complimentary?
Angle A and B are supplementary. If ∠𝐴 measures 970 what is the measure of ∠𝐵?
What is 𝑚∠𝐴?
20.
21.
22.
23.
What is the supplement of 90?
If 𝑚∠1 =480 and 𝑚∠2 = 420 are these angles supplementary?
What is the complement of 840? Supplement?
Using what you know about vertical angles, find the measure of the missing angles. You must be
able to explain why.
24. Parallel lines m and n are cut by a transversal l. If the measure of angle 5 is 680 determine the
measures of the remaining angles. You must be able to explain why.
Circles
Classwork
25. Given the circle to the right, decide whether each line segment is the
radius, diameter or chord.
a. AB : __________________

b.
PQ : __________________
c.
XY : __________________
 the circle to the right, decide whether each line segment is the radius,
26. Given
diameter or chord.

a. AB : __________________

27.
28.
29.
30.
b.
PQ : __________________
c.
XY : __________________
If
the radius of a circle is 25 cm, what is the diameter?
If the radius of a circle is 3.4 m, what is the diameter?
If
the diameter of a circle is 54 cm, what is the radius?
If the diameter of a circle is 7.2 in, what is the radius?
Homework
31. Given the circle to the right, decide whether each line
segment is the radius, diameter or chord.
a. AB : __________________

b.
PQ : __________________
c.
XY : __________________
32.
 Given the circle to the right, decide whether each line segment is the radius, diameter or chord.
a. AB : __________________


b.
PQ : __________________
c.
XY : __________________
33.
 If the radius of a circle is 23 inches, what is its diameter?
34. If the radius of a circle is 4.7 m, what is its diameter?
35.
 If the diameter of a circle is 18 m, what is its radius?
36. If the diameter of a circle is 8 feet, what is its radius?
Polygons
Classwork
37. What is the name of a polygon that has 4 sides? 8 sides? 10 sides?
For each figure complete the following:
a. Determine whether or not it is a polygon
b. If it is not a polygon, explain why not. If it is a polygon, name it and determine whether it
is regular.
38.
39.
40.
41.
42.
43.
Homework
44. What is the name of a polygon that has 3 sides? 6 sides? 9 sides?
For each figure complete the following:
a. Determine whether or not it is a polygon
b. If it is not a polygon, explain why not. If it is a polygon, name it and determine whether it
is regular.
45.
46.
47.
48.
49.
50.
Sum of Angles
Classwork
51. For each polygon below, determine how many triangles the polygon can be divided into AND the sum
of the interior angles.
a.
b.
c.
52. For each figure, find the measure of the missing angles:
a.
b.
Homework
53. For each polygon below, determine how many triangles the polygon can be divided into AND the sum
of the interior angles.
a.
b.
c.
54. For each figure, find the measure of the missing angles:
a.
b.
Classifying Triangles and Quadrilaterals
Classwork
Classify each triangle by its angles AND sides:
55.
56.
57.
58.
59. Draw a right triangle. Classify it based on its sides.
Give every name that describes each figure. Then underline the name that best describes the figure.
60.
61.
61.
62.
63.
64.
65. Draw a rhombus. Write all names that describe the figure.
Homework
Classify each triangle by its angles AND sides:
66.
67.
68.
69. Draw an equilateral triangle. Classify it by its angles.
Give every name that describes each figure. Then underline the name that best describes the figure.
70.
71.
72.
73.
74. Draw a square. Write all the names that describe the square.
Perimeter and Circumference
Classwork
Find the perimeter of each figure.
75.
76.
77.
78.
79.
80.
81.
82.
83.
Determine the circumference of a circle with radius 5 cm.
Determine the circumference of a circle with radius 2.3 m.
Determine the circumference of a circle whose diameter is 8 m.
Determine the circumference of a circle whose diameter is 24.6 cm.
What is the diameter of a circle whose circumference is 47.1 m?
Homework
Find the perimeter of each figure.
84.
85.
86.
87.
88.
89.
90.
91.
92.
Determine the circumference of a circle whose radius is 3.5 m.
Determine the circumference of a circle whose radius is 32 inches.
Determine the circumference of a circle whose diameter is 32 inches.
Determine the circumference of a circle with diameter 8 feet.
What is the radius of a circle whose circumference is 13.188 cm?
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
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18.
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21.
22.
23.
24.
Yes
48°
27°
18°
Yes
65°
128°
108°
Yes
Complement = 22°, Supplement = 112°
Multiple answers for the reasons. Some examples:
<b = 65° since it's vertical to a 65° angle and vertical angles are congruent
<c = 115° since it's supplemental to <b and to the 65° angle
<d = 115° since it's vertical to <c or supplemental to <b
Multiple answers for the reasons. Some examples:
<1 = 37° since it's an alternate exterior angle to <5 and alternate exterior angles are congruent
<2 = 143° since it's supplemental to <1
<3 = 37° since it's vertical to <5
<4 = 143° since it's supplemental to <3 and <5 or since it corresponds to <2
<6 = 143° since it's vertical to <4 or since it's an alternate interior angle to <2
<7 = 37° since it's vertical to <1 or since it's an alternate interior angle to <3
<8=143° since it's vertical to <2 or an alternate exterior angle to <4 or corresponds to <6
No
64°
72°
81°
No
83°
70°
171°
No
Complement = 6°, Supplement = 96°
Multiple answers for the reasons. Some examples:
<b = 40° since it's vertical to a 40° angle and vertical angles are congruent
<c = 140° since it's supplemental to <b
<a = 140° since it's vertical to <c or supplemental to the 40° angle
Multiple answers for the reasons. Some examples:
<1 = 68° since it's an alternate exterior angle to <5
<2 = 112° since it's supplemental to <1
<3 = 68° since it's vertical to <5 or corresponds to <1
<4 = 112° since it's supplemental to <3 and <5
<6 = 112° since it's supplemental to <5 or vertical to <4 or an alternate interior angle to <2
<7 = 68° since it's vertical to <1 or an alternate interior angle to <3
<8 = 112° since it's vertical to <2 or an alternate exterior angle to <4
25.
a. Chord
b. Radius
c. Chord
26.
27.
28.
29.
30.
a. Diameter
b. Radius
c. Chord
50 cm
6.8 m
27 cm
3.6 in
31.
a. Diameter
b. Chord
c. Chord
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
a. Chord
b. Diameter
c. Radius
46 in
9.4 in
9m
4 ft
4 sides = Quadrilateral, 8 sides = Octagon, 10 sides = Decagon
Polygon; Regular Hexagon
Polygon, Irregular Heptagon
Polygon, Irregular Quadrilateral
Not a Polygon since it has a curved line
Polygon, Irregular Nonagon
Polygon, Irregular Pentagon
3 sides = Triangle, 6 sides = Hexagon, 9 sides = Nonagon
Polygon, Regular Triangle
Polygon, Irregular Pentagon
Not a Polygon since not all sides are straight
Polygon, Irregular Pentagon
Polygon, Irregular Pentagon
Polygon, Regular Hexagon
a. 2 triangles, 360°
b. 6 triangles, 1080°
c. 5 triangles, 900°
52.
a. 27°
b. <T = 145°, <S = 35°, 3rd missing angle = 35°
53.
a. 5 triangles, 900°
b. 7 triangles, 1260°
c. 3 triangles, 540°
54.
55.
56.
57.
58.
59.
a. 85°
b. 135°
Acute, Equilateral
Acute, Scalene
Right, Isosceles
Acute, Scalene
Multiple Answers:
Scalene
60.
61.
62.
63.
64.
Isosceles
Polygon, Quadrilateral, Trapezoid
Polygon, Quadrilateral, Parallelogram, Rhombus
Polygon, Quadrilateral, Parallelogram, Rectangle
Polygon, Quadrilateral
Polygon, Quadrilateral, Parallelogram, Rectangle, Rhombus, Square
65. Polygon, Quadrilateral, Parallelogram, Rhombus
66.
67.
68.
69.
Acute, Isosceles
Obtuse, Scalene
Right, Scalene
Acute
70.
71.
72.
73.
74.
Polygon, Quadrilateral, Parallelogram, Rhombus
Polygon, Quadrilateral, Trapezoid
Polygon, Quadrilateral, Parallelogram
Polygon, Quadrilateral
Polygon, Quadrilateral, Parallelogram, Rectangle, Rhombus, Square
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
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90.
91.
92.
10 m
16 ft
16 in
24 m
31.4 cm
14.444 m
25.12 m
77.244 cm
15 m
42 cm
100 m
18 ft
64 m
21.98 m
200.96 in
100.48 in
25.12 ft
2.1 cm