Name: ________________________ Class: ___________________ Date: __________
ID: A
Pythagorean Theorem and Special Rights
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Find the length of the missing side. The triangle is not drawn to scale.
____
____
____
1.
a.
169
b.
13
c.
60
d.
34
a.
6
b.
36
c.
13
d.
4
2.
3. Triangle ABC has side lengths 9, 40, and 41. Do the side lengths form a Pythagorean triple? Explain.
a. No, they do not form a Pythagorean triple; 9 2 + 40 2 ≠ 41 2 .
b. No, they do not form a Pythagorean triple; although 9 2 + 402 = 41 2 , the side lengths do
not meet the other requirements of a Pythagorean triple.
c. Yes; they can form a right triangle, so they form a Pythagorean triple.
d. Yes, they form a Pythagorean triple; 9 2 + 402 = 41 2 and 9, 40, and 41 are all nonzero
whole numbers.
1
Name: ________________________
ID: A
Find the length of the missing side. Leave your answer in simplest radical form.
____
____
4.
a.
73 cm
b.
17 cm
c.
a.
5 ft
b.
493 ft
c.
73 cm
d.
13 cm
d.
155 ft
5.
31 ft
____
6. A grid shows the positions of a subway stop and your house. The subway stop is located at (1, 9) and your
house is located at (–5, –3). What is the distance, to the nearest unit, between your house and the subway
stop?
a. 13
b. 10
c. 18
d. 23
____
7. Find the length of the hypotenuse.
a.
12
b.
6
c.
2
5
d.
18
Name: ________________________
____
8. In triangle ABC, ∠A is a right angle and m∠B = 45°. Find BC. If your answer is not an integer, leave it in
simplest radical form.
a.
____
ID: A
14
2 ft
b.
7
2 ft
c.
14 ft
d.
7 ft
9. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to
the nearest tenth.
a.
x = 4.2, y = 3
b.
x = 2.1, y = 2.6
c.
x = 2.6, y = 2.1
____ 10. The area of a square garden is 200 m2. How long is the diagonal?
a. 20 m
b. 400 m
c. 10 6 m
d.
x = 3, y = 4.2
d.
100 m
____ 11. The length of the hypotenuse of a 30°–60°–90° triangle is 9. Find the perimeter.
c. 9 + 27 3
a. 27 + 9 3
27 9
9 27
b.
+
3
d.
+
3
2
2
2 2
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
____ 12.
a.
2
b.
14 3
c.
3
7 3
d.
1
2
Name: ________________________
ID: A
____ 13.
Not drawn to scale
a.
x = 36 3 , y = 12
c.
x = 12 3 , y = 36
b.
x = 12, y = 36 3
d.
x = 36, y = 12 3
____ 14. A piece of art is in the shape of an equilateral triangle with sides of 25 in. Find the area of the piece of art.
Round your answer to the nearest tenth.
a. 541.3 in.2
b. 270.6 in.2
c. 221 in.2
d. none of these
____ 15. A conveyor belt carries supplies from the first floor to the second floor, which is 23 feet higher. The belt makes
a 60° angle with the ground.
How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the
nearest foot.
If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to
the second floor?
a. 40 ft; 34 min
b. 13 ft; 1 min
c. 27 ft; 0.4 min
d. 33 ft; 20.3 min
Essay
16. A 16-foot ladder is placed against the side of a building as shown in Figure 1 below. The bottom of the ladder
is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, the
ladder is moved 4 feet closer to the base of the building, as shown in Figure 2.
To the nearest foot, how much farther up the building does the ladder now reach? Show how you arrived at
your answer.
4
Name: ________________________
ID: A
17.
a.
b.
Find the area of a regular hexagon with sides 2 cm long. Leave your answer in simplest
radical form.
Use your answer from part (a) to find the area of a regular hexagon of side length 8.
5
ID: A
Pythagorean Theorem and Special Rights
Answer Section
MULTIPLE CHOICE
1. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
2. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
3. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
4. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
5. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
6. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
DOK:
7. ANS:
OBJ:
NAT:
KEY:
B
PTS: 1
DIF: L2
8-1 The Pythagorean Theorem and Its Converse
8-1.1 Use the Pythagorean Theorem and its converse
CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d
STA: 2.5.c| 4.2.a| 6.2.a
8-1 Problem 1 Finding the Length of the Hypotenuse
Pythagorean Theorem | leg | hypotenuse
DOK: DOK 1
A
PTS: 1
DIF: L3
8-1 The Pythagorean Theorem and Its Converse
8-1.1 Use the Pythagorean Theorem and its converse
CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d
STA: 2.5.c| 4.2.a| 6.2.a
8-1 Problem 2 Finding the Length of a Leg
Pythagorean Theorem | leg | hypotenuse
DOK: DOK 1
D
PTS: 1
DIF: L3
8-1 The Pythagorean Theorem and Its Converse
8-1.1 Use the Pythagorean Theorem and its converse
CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d
STA: 2.5.c| 4.2.a| 6.2.a
8-1 Problem 1 Finding the Length of the Hypotenuse
Pythagorean Theorem | leg | hypotenuse
DOK: DOK 1
A
PTS: 1
DIF: L3
8-1 The Pythagorean Theorem and Its Converse
8-1.1 Use the Pythagorean Theorem and its converse
CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d
STA: 2.5.c| 4.2.a| 6.2.a
8-1 Problem 1 Finding the Length of the Hypotenuse
Pythagorean Theorem | leg | hypotenuse
DOK: DOK 1
D
PTS: 1
DIF: L3
8-1 The Pythagorean Theorem and Its Converse
8-1.1 Use the Pythagorean Theorem and its converse
CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d
STA: 2.5.c| 4.2.a| 6.2.a
8-1 Problem 2 Finding the Length of a Leg
Pythagorean Theorem | leg | hypotenuse
DOK: DOK 1
A
PTS: 1
DIF: L3
8-1 The Pythagorean Theorem and Its Converse
8-1.1 Use the Pythagorean Theorem and its converse
CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d
STA: 2.5.c| 4.2.a| 6.2.a
8-1 Problem 3 Finding Distance
Pythagorean Theorem | leg | hypotenuse | word problem | problem solving
DOK 2
B
PTS: 1
DIF: L3
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 1 Finding the Length of the Hypotenuse
special right triangles | hypotenuse DOK: DOK 1
1
ID: A
8. ANS:
OBJ:
NAT:
KEY:
9. ANS:
OBJ:
NAT:
KEY:
10. ANS:
OBJ:
NAT:
DOK:
11. ANS:
OBJ:
NAT:
KEY:
12. ANS:
OBJ:
NAT:
KEY:
13. ANS:
OBJ:
NAT:
KEY:
14. ANS:
OBJ:
NAT:
KEY:
15. ANS:
OBJ:
NAT:
KEY:
DOK:
B
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 1 Finding the Length of the Hypotenuse
special right triangles
DOK: DOK 1
A
PTS: 1
DIF: L4
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 2 Finding the Length of a Leg
special right triangles | hypotenuse | leg
DOK: DOK 1
A
PTS: 1
DIF: L4
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 3 Finding Distance
KEY: special right triangles | diagonal
DOK 2
B
PTS: 1
DIF: L4
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 4 Using the Length of One Side
special right triangles | perimeter
DOK: DOK 3
C
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 4 Using the Length of One Side
special right triangles | leg | hypotenuse
DOK: DOK 2
D
PTS: 1
DIF: L3
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 4 Using the Length of One Side
special right triangles | leg | hypotenuse
DOK: DOK 2
B
PTS: 1
DIF: L2
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 5 Applying the 30º-60º-90º Triangle Theorem
area of a triangle | word problem | problem solving
DOK: DOK 2
C
PTS: 1
DIF: L4
REF: 8-2 Special Right Triangles
8-2.1 Use the properties of 45-45-90 and 30-60-90 triangles
CC G.SRT.8 TOP: 8-2 Problem 5 Applying the 30º-60º-90º Triangle Theorem
special right triangles | multi-part question | word problem | problem solving
DOK 3
2
ID: A
ESSAY
16. ANS:
[4] Answers may vary. Sample:
The height of the ladder by the first building is
8 2 + h 2 = 16 2
h 2 = 192
h = 192
The height of the ladder by the second building is
4 2 + h 2 = 16 2
h 2 = 240
h =
240
240 − 192 ≈ 2
The second ladder goes about 2 feet higher than the first ladder.
[3] correct methods, but error in computation
[2] error in method used
[1] correct answer but work not shown
PTS:
OBJ:
NAT:
TOP:
KEY:
DOK:
1
DIF: L3
REF: 8-1 The Pythagorean Theorem and Its Converse
8-1.1 Use the Pythagorean Theorem and its converse
CC G.SRT.4| CC G.SRT.8| N.5.e| G.3.d
STA: 2.5.c| 4.2.a| 6.2.a
8-1 Problem 3 Finding Distance
Pythagorean Theorem | extended response | rubric-based question | word problem | problem solving
DOK 2
3
ID: A
17. ANS:
[4] Answers may vary. Sample:
360
a.
= 60°. The
The central angle of one of the triangles in the hexagon is
60
altitude of the triangle is
3 because it is a 30°–60°–90° right triangle.
1
[3]
[2]
[1]
Ê
ˆ
(2) ÁÁÁ 3 ˜˜˜ or 6 3 cm2 .
Ë
¯
2
b. Because regular hexagons are similar, their areas will be proportional to the
2
ÁÊÁ 1 ˆ˜˜
1
6 3
Á
˜
square of their similarity ratio: ÁÁÁ ˜˜˜ =
=
. x = 96 3 cm2.
ÁË 4 ˜¯
16
x
correct methods but with a minor computational error
error in method
correct answer but with no work shown
PTS:
OBJ:
NAT:
TOP:
KEY:
DOK:
1
DIF: L4
REF: 10-4 Perimeters and Areas of Similar Figures
10-4.1 Find the perimeters and areas of similar polygons
CC G.SRT.5| N.3.c| N.3.f| M.1.c| M.1.f| A.4.e
STA: 2.3.c| 2.5.b| 2.5.c| 4.2.b
10-4 Problem 4 Finding Perimeter Ratios
area of a triangle | similar figures | similarity ratio | extended response | rubric-based question
DOK 3
The area of the hexagon is therefore 6 ×
4