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 is 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 10 and the other is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 10² + 12²; c² = 100 + 144; c² = 244; c = √244 ≈ 15.6.

Front

Is side 'a' always the longest side in a right triangle?

Back

No, side 'c' (the hypotenuse) is always the longest side in a right triangle.

Front

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

Back

To find the length of a missing side, use the formula: a² + b² = c², where c is the hypotenuse.

Front

If a right triangle has sides of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = √100 = 10.

Front

Can the Pythagorean Theorem be used for obtuse triangles?

Back

No, the Pythagorean Theorem cannot be used for obtuse triangles.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

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

Back

It is an isosceles right triangle.

Front

What is the length of the missing side if one side is 7.2 km and the hypotenuse is 10 km?

Back

Using the Pythagorean Theorem: c² = a² + b²; 10² = 7.2² + b²; 100 = 51.84 + b²; b² = 48.16; b ≈ 6.9 km.