Pythagorean Theorem (4B)

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

If one leg of a right triangle is 3 cm and the other leg is 4 cm, what is the length of the hypotenuse?

Back

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

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 and a and b are the legs.

Front

How do you find the length of a leg if you know the hypotenuse and the other leg?

Back

Rearrange the Pythagorean Theorem: a² = c² - b², then take the square root to find a.

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

In a 5-12-13 triangle, 5 and 12 are the legs, and 13 is the hypotenuse. It satisfies the Pythagorean Theorem: 5² + 12² = 13².

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Front

If the hypotenuse of a right triangle is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8 cm.

Front

What is the converse of the Pythagorean Theorem?

Back

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