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: c² = a² + b².

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side. It is a theorem that states if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

How do you find the hypotenuse of a right triangle?

Back

To find the hypotenuse of a right triangle, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

If the legs of a right triangle are 6 and 8, what is the length of the hypotenuse?

Back

The hypotenuse is 10, calculated using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is a special right triangle?

Back

A special right triangle is a triangle with specific angle measures that allow for easy calculation of side lengths. The two most common types are the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side ratios of a 45-45-90 triangle?

Back

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

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is opposite the 90° angle.

Front

If a right triangle has a hypotenuse of 13 and one leg of 5, what is the length of the other leg?

Back

The length of the other leg is 12, calculated using the Pythagorean Theorem: b = √(13² - 5²) = √(169 - 25) = √144 = 12.

Front

What is the relationship between the angles in similar triangles?

Back

In similar triangles, corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

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

Back

To determine if three lengths can form a triangle, use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side.