Pythagorean Theorem and Distance Formula

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 is the formula for calculating distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

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

Tags

CCSS.8.G.B.7

Front

What is the relationship between the areas of the squares on the sides of a right triangle?

Back

The sum of the areas of the two smaller squares is equal to the area of the large square (hypotenuse).

Tags

CCSS.8.G.B.8

Front

Calculate the distance between the points (2, -75) and (10, 235).

Back

Using the distance formula: d = √((10 - 2)² + (235 - (-75))²) = √(8² + 310²) = √(64 + 96100) = √96164 ≈ 310.1.

Tags

CCSS.HSG.GPE.B.7

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Tags

CCSS.4.G.A.2

Front

If the lengths of the two legs of a right triangle are 5 cm and 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13 cm.

Tags

CCSS.8.G.B.7

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

Using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.