12.5 Pythagorean Theorem Review

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 hypotenuse in a right triangle?

Back

The hypotenuse is the side opposite the right angle in a right triangle and is the longest side.

Front

If one side of a right triangle is 6 units and the other side is 8 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 units.

Tags

CCSS.8.G.B.7

Front

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

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c², where a and b are the lengths of the two legs, and c is the length of the hypotenuse.

Tags

CCSS.8.G.B.7

Front

In a right triangle, if the hypotenuse is 13 units and one leg is 5 units, how do you find the other leg?

Back

Use the Pythagorean Theorem: b² = c² - a²; b² = 13² - 5²; b² = 169 - 25; b² = 144; b = 12 units.

Tags

CCSS.8.G.B.7

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5².

Tags

CCSS.8.G.B.8

Front

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

Back

You can use the Pythagorean Theorem: if a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

If a right triangle has legs of lengths 7 and 24, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 7² + 24²; c² = 49 + 576; c² = 625; c = 25 units.

Tags

CCSS.8.G.B.7