Pythagorean Theorem- Missing Sides, Converse

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 can be expressed as: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the formula to find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem: a² + b² = c². Rearrange the formula to solve for the missing side.

Tags

CCSS.8.G.B.7

Front

If one side of a right triangle is 3 and the other is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; c² = 25; c = 5.

Tags

CCSS.8.G.B.7

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

Front

How can you determine if a triangle is obtuse using side lengths?

Back

If the square of the longest side (c) is greater than the sum of the squares of the other two sides (a and b), then the triangle is obtuse: c² > a² + b².

Tags

CCSS.HSG.CO.C.10

Front

How can you determine if a triangle is acute using side lengths?

Back

If the square of the longest side (c) is less than the sum of the squares of the other two sides (a and b), then the triangle is acute: c² < a² + b².

Tags

CCSS.HSG.CO.C.10

Front

Which set of side lengths forms a right triangle? 5, 12, 13

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Tags

CCSS.8.G.B.8

Front

Which set of side lengths does not form a right triangle? 8, 15, 20

Back

No, because 8² + 15² = 64 + 225 = 289, which is not equal to 20² (400).

Tags

CCSS.8.G.B.8

Front

What is the length of the missing side if one side is 6 and the hypotenuse is 10?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8.

Tags

CCSS.8.G.B.7

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Tags

CCSS.8.G.B.8