AnswersGeometry - Semester 1 PathwaysTriangle Similarity: SSS and SAS (Sec 7-3, 7-4, 7-5)

Triangle Classification Theorems Answers

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1
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Ariel completed the work below to show that a triangle with side lengths of 9, 15, and 12 does not form a right triangle. Is Ariel’s answer correct?

Question illustration
A
No, Ariel should have added 122 and 152 and compared that to 92.
B
No, Ariel should have subtracted 122 from 92 and compared that to152.
C
No, Ariel should have added 92 and 122 and compared that to 152.
D
Yes, Ariel’s work is correct.
2
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Which numbers are perfect squares? Check all that apply.

A
1
B
2
C
16
D
18
E
32
F
44
G
94
H
100
3

Anja is creating a triangle using three straws. The two shorter straws have lengths of 20 cm and 21 cm. How long, in centimeters, should the third straw be for Anja to create a right triangle?

Answer not available
4

What is the length of the hypotenuse, x, if (12, 35, x) is a Pythagorean triple?

A
33
B
37
C
47
D
58
5

Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.Step 1: Find the greatest common factor of the given lengths: 7Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct?

Question illustration
A
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
B
Yes, any set of lengths with a common factor is a Pythagorean triple.
C
No, the lengths of Pythagorean triples cannot have any common factors.
D
No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not.
6

Which equation can be used to find x, the length of the hypotenuse of the right triangle?

Question illustration
A
18 + 24 = x
Option A
B
18 squared + 24 = x
Option B
C
(18 + 24) squared = x squared
Option C
D
18 squared + 24 squared = x squared
Option D
7

Which real-world scenario involves a right triangle?

A
a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches
B
a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles
C
a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards
D
a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet
8

Imara used these steps to find the length of the hypotenuse of the right triangle.Step 1: Find the area of the square with side lengths of 20: 400 Step 2: Find the area of the square with side lengths of 15: 225Step 3: Find the sum of the areas of the two squares: 625Step 4: State the length of the hypotenuse: 625Which best describes Imara’s error?

Question illustration
A
She should have found the area of the square with side lengths of 15 first.
B
She did not correctly calculate the area of the square with side lengths of 15.
C
She should have found the sum of 15 and 20 and then squared the sum.
D
She did not find the side lengths of the square with an area of 625.
9

Which equation can be used to find x, the length of the hypotenuse of the right triangle?

Question illustration
A
16 + 63 = x
Option A
B
16 squared + 63 = x
Option B
C
(16 + 63) squared = x squared
Option C
D
16 squared + 63 squared = x squared
Option D
10

Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that .Which best describes Nadia’s solution?

Question illustration
A
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
B
She is incorrect because she should have used 45 as the length of the hypotenuse.
C
She is incorrect because she should have squared each leg length and then found the sum.
D
She is correct because the hypotenuse is the longest side of the triangle.

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