Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: c² = a² + b².

Tags

CCSS.8.G.B.8

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Tags

CCSS.8.G.B.8

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (using the Pythagorean Theorem: 3² + 4² = c², so 9 + 16 = c², thus c = 5).

Tags

CCSS.8.G.B.8

Front

What is the length of the hypotenuse if the other two sides are 6 cm and 8 cm?

Back

The hypotenuse is 10 cm (6² + 8² = c², so 36 + 64 = c², thus c = 10).

Tags

CCSS.8.G.B.7

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

What is the formula for the Pythagorean Theorem?

Back

The formula is c² = a² + b².

Tags

CCSS.8.G.B.8

Front

If c = 13 and a = 5, what is b?

Back

b = 12 (using the Pythagorean Theorem: 5² + b² = 13², so 25 + b² = 169, thus b = 12).

Tags

CCSS.8.G.B.8

Front

What are the sides of a 30-60-90 triangle in relation to each other?

Back

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.

Tags

CCSS.HSG.CO.C.10

Front

If a right triangle has legs of length 9 and 12, what is the length of the hypotenuse?

Back

The hypotenuse is 15 (9² + 12² = c², so 81 + 144 = c², thus c = 15).

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a right triangle?

Back

The sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Tags

CCSS.8.G.B.8