Copy of Special Right Triangles

Front

What is a special right triangle?

Back

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

Front

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

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 a leg.

Front

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

Back

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

Front

How can you determine if a triangle is acute, right, or obtuse based on side lengths?

Back

Use the Pythagorean theorem: If a² + b² = c², the triangle is right; if a² + b² > c², it is acute; if a² + b² < c², it is obtuse.

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): a² + b² = c².

Front

If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

Back

It is a right triangle, since 5² + 12² = 13².

Front

If a triangle has sides of lengths 8, 15, and 17, what type of triangle is it?

Back

It is a right triangle, since 8² + 15² = 17².

Front

If a triangle has sides of lengths 7, 24, and 25, what type of triangle is it?

Back

It is a right triangle, since 7² + 24² = 25².

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) can be found using the formula d = √(width² + height²).

Front

What is the length of the diagonal of a rectangle with a width of 8 inches and a height of 11 inches?

Back

The diagonal is √(8² + 11²) = √(64 + 121) = √185 ≈ 13.6 inches.