Test 7-1 Review

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). Formula: a² + b² = c².

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45°, 45°, and 90°. The lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

What is a 30-60-90 triangle?

Back

A 30-60-90 triangle is a special right triangle with angles of 30°, 60°, and 90°. The lengths of the sides are in the ratio 1:√3:2, where the shortest side is opposite the 30° angle.

Front

How do you find the length of the hypotenuse in a right triangle?

Back

Use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

What is the formula to find the area of a triangle?

Back

Area = 1/2 * base * height.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if the legs are of length x, then the hypotenuse is x√2.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, if the shortest side (opposite the 30° angle) is x, then the longer leg (opposite the 60° angle) is x√3, and the hypotenuse is 2x.

Front

How do you solve for a missing side in a right triangle?

Back

Use the Pythagorean Theorem or the properties of special triangles (45-45-90 or 30-60-90) depending on the triangle type.

Front

What is the definition of a hypotenuse?

Back

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

Front

What is the significance of the right angle in a triangle?

Back

The right angle (90°) indicates that the triangle is a right triangle, allowing the use of the Pythagorean Theorem.