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: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on 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 one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Front

Can a triangle with sides of lengths 10 cm, 11 cm, and 13 cm form a right triangle?

Back

No, because 10² + 11² does not equal 13² (100 + 121 ≠ 169).

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).

Front

In a right triangle, if one leg is 5 units and the hypotenuse is 13 units, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12 units.

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 legs equals the square of the hypotenuse.

Front

If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, is it a right triangle?

Back

Yes, because 6² + 8² = 10² (36 + 64 = 100).

Front

What is an example of a real-world application of the Pythagorean Theorem?

Back

Finding the distance between two points on a coordinate plane, such as the distance a plane travels north and east.