Geometry Chapter 8 Test

Front

What is the formula to find the length of the altitude (CD) to the hypotenuse (AB) in a right triangle?

Back

CD = √(AD * DB) where AD and DB are the segments of the hypotenuse.

Front

In a right triangle, if one leg is 4 and the other leg is 16, what is the length of the hypotenuse?

Back

Hypotenuse = √(4² + 16²) = √(16 + 256) = √272 = 16.49.

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse.

Front

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

Back

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

Front

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

Back

The sides are in the ratio 1:√3:2.

Front

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

Back

The sides are in the ratio 1:1:√2.

Front

If x = 16, what is the value of z if z = x/4?

Back

z = 16/4 = 4.

Front

What is the area of a triangle given the base and height?

Back

Area = 1/2 * base * height.

Front

What is the definition of an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the definition of a hypotenuse?

Back

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