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: c² = a² + b².

Front

In a right triangle, if one side is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

5 units (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

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 the hypotenuse is 10 units and one side is 6 units, how do you find the other side?

Back

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

Front

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

Back

c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has sides of length 5 and 12, what is the length of the hypotenuse?

Back

13 units (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What do you do to both sides of the equation to solve for a side in the Pythagorean Theorem?

Back

Take the square root of both sides.

Front

In a right triangle, if the lengths of the two legs are equal, what type of triangle is it?

Back

It is an isosceles right triangle.

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.

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.