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

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides. If a² + b² = c² holds true, then it is a right triangle.

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

If a triangle has sides of lengths 15, 30, and 34, is it 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 is equal to 15² (225).

Front

What is the length of the hypotenuse if the legs are 6 cm and 8 cm?

Back

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

Front

What is the length of one leg if the hypotenuse is 10 cm and the other leg is 6 cm?

Back

Using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8 cm.

Front

What is the area of a right triangle with legs of lengths 5 cm and 12 cm?

Back

The area of a right triangle is given by (1/2) * base * height. Here, Area = (1/2) * 5 * 12 = 30 cm².