Triangle Classification Theorems

Question 1

We are given a2 + b2 = c2 for △ABC and right △DEF constructed with legs a and b and hypotenuse n. Since △DEF is a right triangle, we know that a2 + b2 = n2 because of the . By substitution, c2 = n2 Using the square root property and the principle root, we can take the square root of both sides to get c = n. By , triangles ABC and DEF are congruent. Since it is given that ∠F is a right angle, then ∠ is also a right angle by CPCTC. Therefore, △ABC is a right triangle by .

Revolt · Accepted Answer

B: Pythagorean theorem

Question 2

Max has sticks of lengths 6, 7, 8, and 10 inches. He wants to make a right triangle for an art project. Which 3 sticks should he use?

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C: 6 in., 8 in., and 10 in.

Question 3

42 is 32 + 32.

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C: less than

Question 4

Triangle JKL is triangle.

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B: an obtuse

Question 5

We are given a2 + b2 = c2 for △ABC and right △DEF constructed with legs a and b and hypotenuse n. Since △DEF is a right triangle, we know that a2 + b2 = n2 because of the . By substitution, c2 = n2 Using the square root property and the principle root, we can take the square root of both sides to get c = n. By , triangles ABC and DEF are congruent. Since it is given that ∠F is a right angle, then ∠ is also a right angle by CPCTC. Therefore, △ABC is a right triangle by .

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B: SSS

Question 6

Therefore, △JKL is .

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A: acute

Question 7

We are given a2 + b2 = c2 for △ABC and right △DEF constructed with legs a and b and hypotenuse n. Since △DEF is a right triangle, we know that a2 + b2 = n2 because of the . By substitution, c2 = n2 Using the square root property and the principle root, we can take the square root of both sides to get c = n. By , triangles ABC and DEF are congruent. Since it is given that ∠F is a right angle, then ∠ is also a right angle by CPCTC. Therefore, △ABC is a right triangle by .

Revolt · Accepted Answer

C: C

Question 8

52 is 32 + 42.

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B: equal to

Question 9

We are given a2 + b2 = c2 for △ABC and right △DEF constructed with legs a and b and hypotenuse n. Since △DEF is a right triangle, we know that a2 + b2 = n2 because of the . By substitution, c2 = n2 Using the square root property and the principle root, we can take the square root of both sides to get c = n. By , triangles ABC and DEF are congruent. Since it is given that ∠F is a right angle, then ∠ is also a right angle by CPCTC. Therefore, △ABC is a right triangle by .

Revolt · Accepted Answer

D: the definition of right triangle

Question 10

Applying the same method, △ABC is .

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B: right

Triangle Classification Theorems Answers

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