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ANSWER KEY
1.
2.
UNIT 5 – GEOMETRY (Study Guide)
In the figure, line x is parallel to line y. Identify the
measures of ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.
∠1
110⁰
∠2
70⁰
∠3
110⁰
∠4
110⁰
∠5
70⁰
∠6
70⁰
∠7
110⁰
How many different triangles, if any, can be drawn with
side lengths of 2 centimeters, 4 centimeters, and 7
centimeters? No triangles … The sum of the two smaller
sides must be greater than the longest side. 2 + 4 is not
greater than 7.
9.
The diameter of a circle is 12 centimeters. What is the
radius of the circle? Radius = 6 cm (Radius is half of the
diameter)
10. Michael plants a circular garden with a diameter of 10
feet. What is the area of his garden? (𝑨 = 𝝅𝒓𝟐 )
First, find the radius. Since diameter is 10ft, the radius is 5ft.
Next, apply formula: 𝑨 = 𝝅𝒓𝟐
A = 3.14(52)
3.14 (25) = 78.5 ft2
11. A circular mirror has a radius of 6 inches. What is the
circumference of the mirror? (C = 2𝝅𝐫)
C = (2)(3.14)(6) = 37.68 in.
The circumference of the mirror is 37.68 in
12. Which is the shape of the cross section formed when the
cone is sliced by a slanted plane, as shown below?
oval/ellipse
3. How many different triangles, if any, can be drawn with
one 40° angle, one 60° angle, and one 80° angle?
Infinitely many … The sum of the interior angles of a
triangle must be equal to 180⁰ (These angle measures
will result in infinitely many triangles).
13. Which shape could not be a cross section for this cube?
A. hexagon
4.
Classify the triangle according to its sides.
9 ft, 16 ft, 9 ft
Isosceles triangle – 2 equal sides
5.
Classify the triangle according to its angles.
45°, 105°, 30°
obtuse triangle – 1 obtuse angle
6. Identify the measure of the unknown angle for a triangle
with angle measures of 35° and 53°. 92° ↔ Add 35 + 53,
then subtract from 180
7.
8.
9.
Identify the measure of the unknown angle for a right
triangle with one angle measure of 62°. 28° ↔ Right
triangle (one angle must measure 90°. Therefore, add
90 + 62, then subtract from 180
Find the sum of the interior angles of a nine-sided
polygon. 180 (n – 2) ↔ 180 (9 – 2) = 1260 (n represents
the number of sides of the polygon)
B. octagon
C. square
D. triangle
14. Which shape could not be a cross section for this
pyramid?
A. circle
B. square
C. trapezoid
D. triangle
15. The dotted lines show how piano wire is used to slice this
cube. What will be the shape of the cross section?
Which is the shape of the cross section formed when the
cylinder is cut by a plane perpendicular to its base?
rectangle
rectangle
16. If the m∠1 = 42°, then find m∠3: 42⁰
Vertically opposite
angles are equal.
19. What is the least amount of wrapping paper needed to
cover a box that measures 18 inches by 15 inches by 3
inches? Find the surface area of the box.
A box is a rectangular prism (6 faces) (2 of each face)
Dimensions 18in, 15in, 3in
2(18)(15) = 540 in2
It will need at least 738 squared inches
of wrapping paper to cover the box.
17. Flora is drawing a pattern for mosaic. What is the area of
the pattern?
Area of parallelogram = b∗h
Area = (8)(20)
= 160 mm2
2(18)(3) = 108 in2
2(3)(15) = 90 in2
S.A
= 738 in2
20. Two cubes with edge lengths 3 cm for the large cube and
2 cm for the small cube are placed on top of each other
as shown. What is the surface area of the resulting
figure?
Find the total surface area of both cubes,
then subtract the overlapping areas that
are not part of the total surface.
6(S2) + 6(S2)
6(32) + 6(22)
54 + 24
=
78 cm2
Subtract overlapping areas
(not part of S. A.) 2(2)(2) =
8 cm2
Surface Area of resulting figure 70 cm2
21. Find the volume of the composite figure shown below
Volume of Triangular Prism =
½ bh∗ 𝒉 = ½ (4 ∗ 6)(6) = 72 in3
18. Find the area of the composite figure.
Area of Rectangle = L∗W
(21)(14) = 294 cm2
Volume = Bh
Area of triangle = ½ b∗h
½ (9)(16) = 72cm2
Volume of Rectangular Prism =
𝒍 ∗ 𝒘 ∗ 𝒉 = (𝟔)(𝟔)(4) = 144 in3
To find the volume of the
composite figure, find the sum
of both prisms:
72 in3 + 144 in3 = 216 in3
22. How may cubic inches of cheese can this plastic
container hold?
Volume = Bh
Volume of Triangular
Prism = ½ bh∗ 𝒉
Find the sum of the area of the rectangle and the
area of the triangle: 294 cm2 + 72cm2 = 366cm2
½ (3 ∗ 5)(2)
7.5(2) = 15 in3
Determine the value of x in each diagram.
IMPORTANT –
Complementary angles
measure 90°
𝟒𝒙 + 𝟗𝒙 – 𝟏 = 𝟗𝟎
𝟏𝟑𝒙 – 𝟏 = 𝟗𝟎
+𝟏 + 𝟏
𝟏𝟑𝒙
𝟗𝟏
=
𝟏𝟑
𝟏𝟑
𝒙 = 𝟕
𝑰𝑴𝑷𝑶𝑹𝑻𝑨𝑵𝑻 – 𝑺𝒕𝒓𝒂𝒊𝒈𝒉𝒕 𝒂𝒏𝒈𝒍𝒆 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒔 𝟏𝟖𝟎°
𝑥 + 3𝑥 + 40 = 180
4𝑥 + 40 = 180
− 40
– 40
4𝑥
140
=
4
4
𝑥 = 35