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). Formula: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

Use the Distance Formula: Distance = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

What is the hypotenuse in a right triangle?

Back

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

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: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Tags

CCSS.8.G.B.7

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Distance = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What is the formula for finding the area of a rectangle?

Back

Area = length × width.

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Front

In a right triangle, if one angle is 90 degrees, what are the other two angles?

Back

The other two angles must add up to 90 degrees, making them complementary.

Tags

CCSS.7.G.B.5

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

If a rectangular field is 40 yards wide and 30 yards long, what is the diagonal distance across the field?

Back

Diagonal = √(40² + 30²) = √(1600 + 900) = √2500 = 50 yards.

Tags

CCSS.8.G.B.8

Front

What is the distance between the points (2, -3) and (2, 5)?

Back

Distance = √((2 - 2)² + (5 - (-3))²) = √(0 + 8²) = √64 = 8.

Tags

CCSS.HSG.GPE.B.7