Pythagorean Identities and Triples

What is the Pythagorean Theorem?

• a² + b = c

• a² + b² = c²

• a + b = √c

• a + b = c²

Tags

CCSS.8.G.B.8

What are the two special right triangles and their side ratios?

• 45-45-90 triangle (1:1:√2) and 30-60-90 triangle (1:√3:2)

• 30-30-30 triangle (1:1:1)

• 45-45-45 triangle (1:1:1)

• 60-60-60 triangle (1:1:1)

Tags

CCSS.8.G.B.8

What are Pythagorean Triples?

• Pythagorean Triples are sets of three positive integers a, b, and c, such that a^2 + b^2 = c^2.

• Pythagorean Triples are sets of three integers a, b, and c, such that a^3 + b^3 = c^3.

• Pythagorean Triples are sets of three positive integers a, b, and c, such that a + b = c.

• Pythagorean Triples are sets of three negative integers a, b, and c, such that a^2 + b^2 = c^2.

Tags

CCSS.8.G.B.8

In a right triangle with sides of length 3, 4, and 5, is it a Pythagorean Triple?

• Maybe

• Sometimes

• Yes

• No

Tags

CCSS.8.G.B.8

What is the formula to find the hypotenuse of a right triangle in terms of the legs using the Pythagorean Theorem?

• c = a * b

• c = a^2 + b^2

• c = sqrt(a^2 + b^2)

• c = a + b

Tags

CCSS.8.G.B.8

What is the Pythagorean Triple for the sides 5, 12, and 13?

• No

• Yes

• Maybe

• Sometimes

Tags

CCSS.8.G.B.8

What is the relationship between the sides of a 45-45-90 special right triangle?

• The two legs are not congruent

• The hypotenuse is equal to the sum of the two legs

• The hypotenuse is equal to the length of one leg divided by 2

• The relationship between the sides of a 45-45-90 triangle is that the two legs are congruent, and the hypotenuse is the length of one leg multiplied by the square root of 2.

Tags

CCSS.8.G.B.8

How can you determine if a set of three numbers is a Pythagorean Triple?

• Square the largest number and check if it equals the sum of the squares of the other two numbers.

• Add the three numbers together and divide by 3 to get the average

• Check if the smallest number squared equals the sum of the squares of the other two numbers

• Multiply the three numbers together and check if the result is a perfect square

Tags

CCSS.8.G.B.8

In a right triangle with sides of length 7, 24, and 25, is it a Pythagorean Triple?

• No

• Maybe

• Sometimes

• Yes

Tags

CCSS.8.G.B.8

What is the Pythagorean identity for sine and cosine?

• sin(theta) * cos(theta) = 1

• sin^2(theta) + cos^2(theta) = 1

• sin(theta) + cos(theta) = 1

• sin^2(theta) - cos^2(theta) = 1

Tags

CCSS.HSF.TF.C.8