Geometry Semester 1 Review

Front

What is a 45-45-90 triangle?

Back

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

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, if you know the length of the short leg (opposite the 30-degree angle), the hypotenuse is twice the length of the short leg.

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 is the relationship between the angles and sides in a right triangle?

Back

In a right triangle, the side opposite the largest angle (90 degrees) is the hypotenuse, and the other two sides are called the legs. The lengths of the sides are related through the Pythagorean theorem.

Front

What is the formula for the area of a triangle?

Back

The area (A) of a triangle can be calculated using the formula: A = 1/2 * base * height.

Front

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

Back

To find a missing side of a right triangle, rearrange the Pythagorean theorem: if you know two sides, use c² = a² + b² to solve for the missing side.

Front

What is the definition of a right triangle?

Back

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

Front

What is the significance of the 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in a specific ratio: the length of the short leg is x, the length of the long leg is x√3, and the hypotenuse is 2x.

Front

How do you calculate the length of the legs in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if the length of the hypotenuse is h, then the length of each leg is h/√2 or h√2/2.

Front

What is the definition of an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.