Right Triangle Review

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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

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

Back

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

Front

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

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1:1:√2. The two legs are equal in length, and the hypotenuse is √2 times the length of each leg.

Front

How do you find the missing side of a right triangle using the Pythagorean Theorem?

Back

To find a missing side, rearrange the Pythagorean Theorem: c² = a² + b². If you know two sides, square them, add them, and take the square root to find the third side.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.

Front

How do you determine if a triangle is acute, right, or obtuse using side lengths?

Back

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

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.