Pythagorean Theorem & Special Right Triangles

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 are the side lengths of a 45-45-90 triangle in relation to each other?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

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

Back

To determine if three lengths can form a right triangle, apply the Pythagorean Theorem. If a² + b² = c² holds true, where c is the longest side, then the lengths can form a right triangle.

Front

What is the height of a cone if the radius is 5 cm and the slant height is 13 cm?

Back

Using the Pythagorean Theorem, h = √(slant height² - radius²) = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.

Front

What is the relationship between the angles in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

If one leg of a right triangle is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Front

What is the formula for the area of a triangle?

Back

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

Front

In a right triangle, if one angle measures 90 degrees, what are the measures of the other two angles?

Back

The other two angles in a right triangle must add up to 90 degrees, making them complementary.

Front

What is the length of the hypotenuse in a 5-12-13 triangle?

Back

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

Front

What is the significance of the 3-4-5 triangle?

Back

The 3-4-5 triangle is a special right triangle that satisfies the Pythagorean Theorem, making it a common example for demonstrating right triangle properties.