Download Math 6 Geometry Study guide Answer Section

Math 6 Geometry Study guide
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Find the missing measure in each triangle. Then
3.
classify the triangle as acute, right, or obtuse.
1.
60°
38°
60°
a.
b.
c.
d.
x°
a.
b.
c.
d.
62; right
52; right
52; acute
42; obtuse
x°
60; acute
90; right
30; acute
60; obtuse
4.
x°
2.
56°
60°
63°
a.
b.
c.
d.
61; right
51; acute
61; acute
65; obtuse
x°
a.
b.
c.
d.
60; obtuse
90; right
30; acute
30; right
c. obtuse, scalene
d. acute, equilateral
5.
8.
46°
42°
9.5
9.5
x°
a.
b.
c.
d.
82; acute
90; right
78; acute
92; obtuse
70°
6.6
a.
b.
c.
d.
Classify each triangle by its angles and by its sides.
6.
4
acute, scalene
right, isosceles
acute, isosceles
acute, equilateral
Find the best name to classify each quadrilateral.
9.
3
a.
b.
c.
d.
obtuse, scalene
right, scalene
right, isosceles
right, equilateral
7.
a.
b.
c.
d.
42°
50°
88°
a. acute, scalene
b. right, scalene
70°
square
rectangle
quadrilateral
parallelogram
d. parallelogram
10.
13.
a.
b.
c.
d.
quadrilateral
rectangle
trapezoid
parallelogram
a.
b.
c.
d.
quadrilateral
rectangle
square
parallelogram
11.
Determine whether each statement is sometimes,
always, or never true.
a.
b.
c.
d.
rhombus
quadrilateral
trapezoid
parallelogram
12.
14. A trapezoid is a quadrilateral.
a. sometimes
b. always
c. never
15. A quadrilateral is a rhombus.
a. sometimes
b. always
c. never
16. A rectangle is a parallelogram.
a. sometimes
b. always
c. never
17. A rectangle is a trapezoid.
a. sometimes
b. always
c. never
18. A parallelogram is an isosceles triangle.
a. sometimes
b. always
c. never
Find the volume of each rectangular prism. Round
to the nearest tenth if necessary.
a. rhombus
b. rectangle
c. quadrilateral
19.
21.
3 mm
16.5 mm
9 mm
13.6 mm
a.
b.
c.
d.
3 mm
7.8 mm
a.
b.
c.
d.
456 mm2
190.2 mm2
380.4 mm2
102.4 mm2
22.
386.1 mm3
193.1 mm3
27.3 mm3
1,003.9 mm3
20.
12.5 yd
3.2 mm
5 yd
8 mm
4 yd
10 mm
a.
b.
c.
d.
a.
b.
c.
d.
3
21.2 mm
320 mm3
128 mm3
256 mm3
Find the surface area of each rectangular prism.
Round to the nearest tenth if necessary.
Short Answer
Tell whether each pair of figures is congruent,
similar, or neither.
23.
2
86 yd
265 yd2
318 yd2
132.5 yd2
24.
26.
4 cm
6 cm
27.
25.
Find the area of each parallelogram. Round to the
nearest tenth if necessary.
28.
24.7 yd
6.3 yd
Find the area of each triangle. Round to the nearest
tenth if necessary.
29.
20 ft
8 ft
30.
31.
6.3 m
10.4 m
32.
33.
6 mi
3 mi
34.
Find the volume of each solid. Round to the nearest
tenth if necessary.
39.
9.3 cm
11.5 cm
14.7 mm
35. height: 80 mm
base: 14 mm
36. height:
in.
base: 10 in.
2.8 mm
6.7 mm
Find the area to the nearest tenth. Use 3.14 for
.
Find the surface area of each solid. Round to the
nearest tenth if necessary.
37.
40.
8 km
15 mm
5 mm
7 mm
38.
6.7 cm
Essay
41. Tanika built a rectangular prism using 1-inch cubes. The prism is 6 cubes long, 3 cubes deep, and 3 cubes high.
a. What is the surface area of the rectangular prism?
b. What is the volume of the rectangular prism?
c. Draw Tanika’s rectangular prism.
Math 6 Geometry Study guide
Answer Section
MULTIPLE CHOICE
1. ANS: B
The triangle is a right triangle. The sum of its angles is 180°.
x + 90 + 38 = 180
x = 52
Feedback
A
B
C
D
What is the sum of the triangle's interior angles?
Correct!
Are all three angles less than 90 degrees?
Does the triangle contain an angle greater than 90 degrees?
PTS: 1
DIF: Basic
OBJ: 10-4.1 Identify triangles.
TOP: Identify triangles.
KEY: Triangles | Identifying triangles
2. ANS: C
The triangle is an acute triangle. The sum of its angles is 180°.
x + 63 + 56 = 180
x = 61
Feedback
A
B
C
D
Does the triangle contain a right angle?
Double check your work and try again.
Correct!
Does the triangle contain an angle greater than 90 degrees?
PTS: 1
DIF: Average
OBJ: 10-4.1 Identify triangles.
TOP: Identify triangles.
KEY: Triangles | Identifying triangles
3. ANS: A
The triangle is an acute triangle. The sum of its angles is 180°.
x + 60 + 60 = 180
x = 60
Feedback
A
B
C
D
Correct!
Does the triangle contain a right angle?
Double check your work and try again. What is the sum of the interior angles of a
triangle?
Does the triangle contain an angle greater than 90 degrees?
PTS: 1
DIF: Average
OBJ: 10-4.1 Identify triangles.
TOP: Identify triangles.
KEY: Triangles | Identifying triangles
4. ANS: D
The triangle is a right triangle. The sum of its angles is 180°.
x + 90 + 60 = 180
x = 30
Feedback
A
B
C
D
Are there any angles greater than 90 degrees?
Double check your work and try again. What is the sum of the interior angles of a
triangle?
Are all the angles less than 90 degrees?
Correct!
PTS: 1
DIF: Average
OBJ: 10-4.1 Identify triangles.
TOP: Identify triangles.
KEY: Triangles | Identifying triangles
5. ANS: D
The triangle is an obtuse triangle. The sum of its angles is 180°.
x + 46 + 42 = 180
x = 92
Feedback
A
B
C
D
Double check your work and try again. What is the sum of the interior angles of a
triangle?
Be careful when solving for x. Try again.
Are all the angles less than 90 degrees? Double check your work and try again.
Correct!
PTS: 1
DIF: Average
OBJ: 10-4.1 Identify triangles.
TOP: Identify triangles.
KEY: Triangles | Identifying triangles
6. ANS: B
The triangle has three unequal sides and a right angle. It is a right, scalene triangle.
Feedback
A
B
C
D
Does the triangle have an angle greater than 90 degrees?
Correct!
Does the triangle have two sides with the same length?
What kinds of sides does an equilateral triangle have?
PTS: 1
DIF: Basic
OBJ: 10-4.2 Classify triangles.
TOP: Classify triangles.
KEY: Triangles | Classifying triangles
7. ANS: A
The triangle has three unequal sides and three angles less than 90°. It is an acute, scalene triangle.
Feedback
A
B
C
D
Correct!
Does the triangle contain a right angle?
Does the triangle have an angle greater than 90 degrees?
What kinds of sides does an equilateral triangle have?
PTS: 1
DIF: Average
OBJ: 10-4.2 Classify triangles.
TOP: Classify triangles.
KEY: Triangles | Classifying triangles
8. ANS: C
The triangle has two equal sides and three angles less than 90°. It is an acute, isosceles triangle.
Feedback
A
B
C
D
Do any of the sides have the same length?
Does the triangle contain a right angle?
Correct!
What kinds of sides does an equilateral triangle have?
PTS: 1
DIF: Average
OBJ: 10-4.2 Classify triangles.
TOP: Classify triangles.
KEY: Triangles | Classifying triangles
9. ANS: A
The figure has four right angles and four congruent sides. It is a square.
Feedback
A
B
C
D
Correct!
What is the name of a rectangle with four congruent sides?
What is a more specific name for the quadrilateral?
What is the name of a parallelogram with four congruent sides and four right angles?
PTS: 1
DIF: Basic
OBJ: 10-5.1 Identify quadrilaterals.
STA: 7.9 | 7.11
TOP: Identify quadrilaterals.
KEY: Quadrilaterals | Identifying quadrilaterals
10. ANS: C
The figure has one pair of opposite sides parallel. It is a trapezoid.
Feedback
A
B
C
D
What is a more specific name for the quadrilateral?
A rectangle has four right angles.
Correct!
A parallelogram has two pairs of opposite sides parallel. What is the name of a
quadrilateral with exactly one pair of opposite sides parallel?
PTS: 1
DIF: Average
OBJ: 10-5.1 Identify quadrilaterals.
STA: 7.9 | 7.11
TOP: Identify quadrilaterals.
KEY: Quadrilaterals | Identifying quadrilaterals
11. ANS: B
The figure is simply a quadrilateral.
Feedback
A
B
C
D
A rhombus is a parallelogram with four congruent sides.
Correct!
Does the figure have a pair of opposite sides that are parallel?
Are the pairs of opposite sides parallel to each other?
PTS: 1
DIF: Average
OBJ: 10-5.1 Identify quadrilaterals.
STA: 7.9 | 7.11
TOP: Identify quadrilaterals.
KEY: Quadrilaterals | Identifying quadrilaterals
12. ANS: D
The figure has two pairs of opposite sides that are congruent. It is a parallelogram.
Feedback
A
B
Are all four sides of the figure congruent?
A rectangle is a parallelogram with four right angles.
C
D
What is a more specific name for the quadrilateral?
Correct!
PTS: 1
DIF: Average
OBJ: 10-5.1 Identify quadrilaterals.
STA: 7.9 | 7.11
TOP: Identify quadrilaterals.
KEY: Quadrilaterals | Identifying quadrilaterals
13. ANS: B
The figure is a parallelogram with four right angles. It is a rectangle.
Feedback
A
B
C
D
What is a more specific name for the quadrilateral?
Correct!
Are all four sides of the figure congruent?
What is the name for a parallelogram with four right angles?
PTS: 1
DIF: Basic
OBJ: 10-5.1 Identify quadrilaterals.
STA: 7.9 | 7.11
TOP: Identify quadrilaterals.
KEY: Quadrilaterals | Identifying quadrilaterals
14. ANS: B
Every trapezoid has four sides, so a trapezoid is always a quadrilateral.
Feedback
A
B
C
Try to draw a trapezoid that is not a quadrilateral.
Correct!
How many sides does a trapezoid have?
PTS: 1
DIF: Basic
OBJ: 10-5.2 Classify quadrilaterals.
STA: 7.9 | 7.11
TOP: Classify quadrilaterals.
KEY: Quadrilaterals | Classifying quadrilaterals
15. ANS: A
A quadrilateral is sometimes a rhombus, but it can also be a trapezoid, or a parallelogram, etc.
Feedback
A
B
C
Correct!
Is it possible to draw a quadrilateral that is not a rhombus?
How many sides does a rhombus have?
PTS: 1
DIF: Average
OBJ: 10-5.2 Classify quadrilaterals.
STA: 7.9 | 7.11
TOP: Classify quadrilaterals.
KEY: Quadrilaterals | Classifying quadrilaterals
16. ANS: B
A rectangle is a parallelogram with four right angles, so it is always a parallelogram.
Feedback
A
B
C
Is it possible to draw a rectangle that is not a parallelogram?
Correct!
Are the opposite sides of a rectangle parallel?
PTS: 1
DIF: Average
OBJ: 10-5.2 Classify quadrilaterals.
STA: 7.9 | 7.11
TOP: Classify quadrilaterals.
KEY: Quadrilaterals | Classifying quadrilaterals
17. ANS: C
A rectangle is a parallelogram and a trapezoid has exactly one pair of opposite sides parallel, so a rectangle can
never be a trapezoid.
Feedback
A
B
C
Is it possible to draw a rectangle with exactly one pair of opposite sides that are
parallel?
How many pairs of opposite parallel sides does a rectangle have?
Correct!
PTS: 1
DIF: Average
OBJ: 10-5.2 Classify quadrilaterals.
STA: 7.9 | 7.11
TOP: Classify quadrilaterals.
KEY: Quadrilaterals | Classifying quadrilaterals
18. ANS: C
A parallelogram has four sides and can never be a triangle.
Feedback
A
B
C
How many sides does a parallelogram have?
Do parallelograms and isosceles triangles have the same number of sides?
Correct!
PTS: 1
DIF: Basic
OBJ: 10-5.2 Classify quadrilaterals.
STA: 7.9 | 7.11
TOP: Classify quadrilaterals.
KEY: Quadrilaterals | Classifying quadrilaterals
19. ANS: A
Sample:
13 cm
5 cm
9 cm
Use the formula V = Bh.
V = (9)(5)(13)
V = 585 cm3
Feedback
A
B
C
D
Correct!
The volume of a prism is the product of the area of its base and its height.
What operation is used to calculate volume?
What is the area of the base of the prism?
PTS: 1
DIF: Average
OBJ: 12-2.1 Find the volumes of rectangular prisms.
STA: 7.8
TOP: Find the volumes of rectangular prisms.
KEY: Volume | Prisms
20. ANS: D
Sample:
6 mm
5.9 mm
8.1 mm
Use the formula V = Bh.
V = (8.1)(5.9)(6)
V = 286.74 mm3
Feedback
A
B
C
D
What operation is used to calculate volume?
What is the area of the base of the prism?
The volume of a prism is the product of the area of its base and its height.
Correct!
PTS: 1
DIF: Average
OBJ: 12-2.1 Find the volumes of rectangular prisms.
STA: 7.8
TOP: Find the volumes of rectangular prisms.
KEY: Volume | Prisms
21. ANS: C
Sample:
6 cm
8.4 cm
10 cm
Find the area of each of the six faces. Add these together to find the total surface area.
SA = 2(10)(8.4) + 2(8.4)(6) + 2(10)(6)
SA = 168 + 100.8 + 120
SA = 388.8 cm2
Feedback
A
B
C
D
Find the area of each of the six faces and add them to find the total surface area.
Be sure to account for all six sides of the prism.
Correct!
What operation is needed to find the area of each face?
PTS: 1
DIF: Average
OBJ: 12-4.1 Find the surface areas of rectangular prisms.
STA: 7.8
TOP: Find the surface areas of rectangular prisms.
KEY: Surface area | Prisms
22. ANS: B
Sample:
15 mm
4 mm
4.4 mm
Find the area of each of the six faces. Add these together to find the total surface area.
SA = 2(4.4)(4) + 2(4)(15) + 2(4.4)(15)
SA = 35.2 + 120 + 132
SA = 287.2 mm2
Feedback
A
B
C
D
What operation is needed to find the area of each face?
Correct!
Find the area of each of the six faces and add them to find the total surface area.
Be sure to account for all six sides of the prism.
PTS: 1
DIF: Average
OBJ: 12-4.1 Find the surface areas of rectangular prisms.
STA: 7.8
TOP: Find the surface areas of rectangular prisms.
KEY: Surface area | Prisms
SHORT ANSWER
23. ANS:
congruent
The two hexagons have the same size and shape. They are congruent figures.
PTS: 1
DIF: Basic
OBJ: 13-6.1 Determine congruence and similarity.
STA: 6.15
TOP: Determine congruence and similarity.
KEY: Congruent | Similar
24. ANS:
neither
The two triangles do not have the same size or the same shape. They are neither congruent nor similar.
PTS: 1
DIF: Average
OBJ: 13-6.1 Determine congruence and similarity.
STA: 6.15
TOP: Determine congruence and similarity.
KEY: Congruent | Similar
25. ANS:
similar
The two octagons have the same shape but different sizes. They are similar figures.
PTS: 1
DIF: Average
OBJ: 13-6.1 Determine congruence and similarity.
STA: 6.15
TOP: Determine congruence and similarity.
KEY: Congruent | Similar
26. ANS:
24 cm2
Use the formula A = bh.
A = 6(4)
A = 24 cm2
PTS: 1
DIF: Basic
OBJ: 14-1.1 Find the areas of parallelograms.
STA: 6.13a | 6.13b TOP: Find the areas of parallelograms.
KEY: Area | Parallelograms
27. ANS:
42 unit2
Use the formula A = bh.
A = 6(7)
A = 42 unit2
PTS: 1
DIF: Average
OBJ: 14-1.1 Find the areas of parallelograms.
STA: 6.13a | 6.13b TOP: Find the areas of parallelograms.
KEY: Area | Parallelograms
28. ANS:
155.6 yd2
Use the formula A = bh.
A = 24.7(6.3)
A = 155.61 yd2
PTS: 1
DIF: Average
OBJ: 14-1.1 Find the areas of parallelograms.
STA: 6.13a | 6.13b TOP: Find the areas of parallelograms.
KEY: Area | Parallelograms
29. ANS:
80 ft2
Use the formula
PTS: 1
STA: 6.13a
30. ANS:
21 unit2
Use the formula
PTS: 1
STA: 6.13a
.
DIF: Average
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
.
DIF: Average
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
31. ANS:
32.8 m2
Use the formula
PTS: 1
STA: 6.13a
32. ANS:
28 unit2
Use the formula
.
DIF: Average
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
.
PTS: 1
STA: 6.13a
33. ANS:
9 mi2
Use the formula
DIF: Average
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
PTS: 1
STA: 6.13a
34. ANS:
53.5 cm2
Use the formula
DIF: Basic
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
PTS: 1
STA: 6.13a
35. ANS:
560 mm2
Use the formula
DIF: Average
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
PTS: 1
STA: 6.13a
36. ANS:
DIF: Average
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
.
.
.
in2
Use the formula
PTS: 1
STA: 6.13a
37. ANS:
50.2 km2
Sample:
.
DIF: Average
OBJ: 14-2.1 Find the areas of triangles.
TOP: Find the areas of triangles.
KEY: Area | Triangles
6 ft
Use the formula
PTS: 1
STA: 6.15 | 6.16
38. ANS:
35.2 cm2
Sample:
. The radius is one half the diameter.
DIF: Basic
OBJ: 14-3.1 Find the areas of circles.
TOP: Find the areas of circles.
KEY: Area | Circles
4.6 ft
Use the formula
.
PTS: 1
STA: 6.15 | 6.16
39. ANS:
275.8 mm3
Sample:
DIF: Average
OBJ: 14-3.1 Find the areas of circles.
TOP: Find the areas of circles.
KEY: Area | Circles
13 ft
4 ft
5 ft
Use the formula V = Bh.
V = (5)(4)(13)
V = 260 ft3
PTS: 1
DIF: Average
OBJ: 14-5.1 Find the volume of rectangular prisms.
TOP: Find the volume of rectangular prisms.
KEY: Volume | Prisms
40. ANS:
430 mm2
Sample:
13 ft
5 ft
9 ft
Find the area of each of the six faces. Add these together to find the total surface area.
SA = 2(9)(5) + 2(5)(13) + 2(9)(13)
SA = 90 + 130 + 234
SA = 454 ft2
PTS: 1
DIF: Basic
OBJ: 14-6.1 Find the surface areas of rectangular prisms.
STA: 6.15
TOP: Find the surface areas of rectangular prisms.
KEY: Surface area | Prisms
ESSAY
41. ANS:
a. 90 in2
Use the surface area formula.
SA = 2(6)(3) + 2(3)(3) + 2(6)(3)
SA = 36 + 18 + 36
SA = 90 in2
b. 54 in3
Use the formula V = Bh.
V = (6)(3)(3)
V = 54 in3
c.
All reasonably drawn prisms should be accepted.
PTS: 1
DIF: Advanced
OBJ: 14-7.1 Solve problems and show solutions.
TOP: Solve problems and show solutions.
KEY: Problem solving | Solutions