Pythagorean 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 is expressed as: c² = a² + b².

Tags

CCSS.8.G.B.8

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.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 c = 10 and a = 6, what is b?

Back

b = 8 (Using the Pythagorean Theorem: 10² = 6² + b² => 100 = 36 + b² => b² = 64 => b = 8).

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Tags

CCSS.8.G.B.8

Front

If a = 5 and b = 12, what is c?

Back

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

Tags

CCSS.8.G.B.8

Front

What does it mean if c² < a² + b²?

Back

If c² < a² + b², the triangle is acute, meaning all angles are less than 90 degrees.

Tags

CCSS.8.G.B.8

Front

What does it mean if c² > a² + b²?

Back

If c² > a² + b², the triangle is obtuse, meaning one angle is greater than 90 degrees.

Tags

CCSS.8.G.B.8

Front

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

Back

To find the length of a side, use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Tags

CCSS.8.G.B.7

Front

If c = 50 and b = 30, what is a?

Back

a = 40 (Using the Pythagorean Theorem: 50² = a² + 30² => 2500 = a² + 900 => a² = 1600 => a = 40).

Tags

CCSS.8.G.B.8