Pythagorean and converse

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 is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

How can you determine if three sides can form a right triangle?

Back

To determine if three sides can form a right triangle, use the Pythagorean Theorem. If a² + b² = c² holds true, then the sides can form a right triangle.

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 side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

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

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and if a² + b² = c², then the triangle is a right triangle.

Front

Can the sides 15, 30, and 34 form a right triangle?

Back

No, because 15² + 30² = 225 + 900 = 1125, which is not equal to 34² (1156).

Front

If a triangle has sides of lengths 9, 12, and 15, is it a right triangle?

Back

Yes, because 9² + 12² = 81 + 144 = 225, which equals 15².

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.

Front

If the base of a right triangle is 5 and the height is 12, what is the area?

Back

Area = (1/2) * 5 * 12 = 30.