Flashcard: Pythagorean Theorem and 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 special right triangles?

Back

The special right triangles are the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is √2 times the length of a leg. In a 30-60-90 triangle, the lengths are in the ratio 1:√3:2.

Front

How do you determine if a set of sides can form a right triangle?

Back

To determine if a set of three sides can form a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides (a² + b² = c²).

Front

If the legs of a right triangle are 10 and 24, what is the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 10² + 24² = 100 + 576 = 676. Therefore, c = √676 = 26.

Front

Solve for x in the right triangle with legs 12 and x, and hypotenuse 13.

Back

Using the Pythagorean Theorem: 12² + x² = 13². This gives 144 + x² = 169, so x² = 25, and x = 5.

Front

What is the length of the hypotenuse in a 30-60-90 triangle with a shorter leg of 5?

Back

In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg. Therefore, the hypotenuse is 2 * 5 = 10.

Front

What is the relationship between the angles in a right triangle?

Back

In a right triangle, one angle is 90 degrees, and the sum of the other two angles is 90 degrees, making the total sum of angles in any triangle equal to 180 degrees.

Front

If one leg of a right triangle is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 8² + b² = 10². This gives 64 + b² = 100, so b² = 36, and b = 6.

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Front

In a 45-45-90 triangle, if one leg is 7, what is the length of the hypotenuse?

Back

In a 45-45-90 triangle, the hypotenuse is √2 times the length of a leg. Therefore, the hypotenuse is 7√2.