Pythagorean Theorem and 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). Formula: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

Front

How do you determine if a triangle is acute, obtuse, or right using side lengths?

Back

1. For a right triangle: a² + b² = c². 2. For an acute triangle: a² + b² > c². 3. For an obtuse triangle: a² + b² < c², where c is the longest side.

Tags

CCSS.HSG.CO.C.10

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (using the Pythagorean Theorem: 3² + 4² = c² => 9 + 16 = c² => c² = 25 => c = 5).

Tags

CCSS.8.G.B.8

Front

What is the length of the missing side if a = 12 in and b = 5 in?

Back

c = 13 in (using the Pythagorean Theorem: 12² + 5² = c² => 144 + 25 = c² => c² = 169 => c = 13).

Tags

CCSS.8.G.B.7

Front

What is the length of the missing side if a = 48 in and b = 36 in?

Back

c = 60 in (using the Pythagorean Theorem: 48² + 36² = c² => 2304 + 1296 = c² => c² = 3600 => c = 60).

Tags

CCSS.8.G.B.7

Front

If the sides of a triangle are 2.8, 19.1, and 19.7, what type of triangle is it?

Back

Obtuse Triangle (since 2.8² + 19.1² < 19.7²).

Tags

CCSS.8.G.B.8

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) * base * height.

Tags

CCSS.6.G.A.1

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

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Tags

CCSS.8.G.B.8