Flashcard - Special Right / Pythg Thm

Front

What is a special right triangle?

Back

A special right triangle is a triangle with specific angle measures and side length ratios, commonly the 45-45-90 triangle and the 30-60-90 triangle.

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): c² = a² + b².

Front

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

Back

In a 30-60-90 triangle, the side opposite the 30° angle is x, the side opposite the 60° angle is x√3, and the hypotenuse is 2x.

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 x, and the hypotenuse is x√2.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is a leg in a right triangle?

Back

A leg is one of the two shorter sides of a right triangle that form the right angle.

Front

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

Back

Use the Pythagorean Theorem: if a² + b² = c², where c is the longest side, then the lengths can form a right triangle.

Front

What is an isosceles right triangle?

Back

An isosceles right triangle has two equal sides and one right angle, with angles measuring 45°, 45°, and 90°.

Front

If one leg of a 45-45-90 triangle is 9, what is the length of the hypotenuse?

Back

The hypotenuse is 9√2.

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The shorter leg is 6.