Unit 5: 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 can be expressed as: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Tags

CCSS.8.G.B.8

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. They are usually referred to as sides a and b.

Front

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

Back

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

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 lengths of the legs equals the square of the length of the hypotenuse.

Tags

CCSS.8.G.B.8

Front

If the hypotenuse of a right triangle is 10 units and one leg is 6 units, how do you find the length of the other leg?

Back

Use the Pythagorean Theorem: c² = a² + b²; 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8 units.

Tags

CCSS.8.G.B.7

Front

What is the formula to find the hypotenuse in a right triangle?

Back

The formula to find the hypotenuse (c) is: c = √(a² + b²).

Tags

CCSS.8.G.B.8

Front

What is the formula to find a leg in a right triangle if the hypotenuse and the other leg are known?

Back

The formula is: a = √(c² - b²) or b = √(c² - a²).

Tags

CCSS.8.G.B.7

Front

In a right triangle, if one leg is 5 units and the hypotenuse is 13 units, what is the length of the other leg?

Back

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

Tags

CCSS.8.G.B.7

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula between two points (x1, y1) and (x2, y2) is: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7