Pythagorean Theorem: Find the Missing Side

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.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle 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 formula to find the length of a missing side in a right triangle?

Back

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

Front

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

Back

Use the formula: a² + 6² = 10². This simplifies to a² + 36 = 100, so a² = 64, and a = 8 units.

Front

What is the length of the missing side if one side is 8 in. and the hypotenuse is 10 in.?

Back

6 in. (using the Pythagorean Theorem: 8² + b² = 10²; 64 + b² = 100; b² = 36; b = 6).

Front

Can the Pythagorean Theorem be used for obtuse triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

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

Back

13 units (5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the two shorter sides equals the square of the hypotenuse.