Chapter 5 Study Guide

Front

What is the incenter of a triangle?

Back

The incenter of a triangle is the point where the angle bisectors of the triangle intersect. It is also the center of the circle inscribed within the triangle.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Given lengths 5, 6, and 9, can a triangle be formed?

Back

Yes! The lengths satisfy the triangle inequality theorem.

Front

Given lengths 3, 4, and 8, can a triangle be formed?

Back

No, because 3 + 4 < 8.

Front

What is the formula to find the length of a side in a triangle using the incenter?

Back

The length of a side can be found using the formula: a = (r * s) / (s - a), where r is the inradius and s is the semi-perimeter.

Front

What is the semi-perimeter of a triangle?

Back

The semi-perimeter (s) of a triangle is half the sum of the lengths of its sides, calculated as s = (a + b + c) / 2.

Front

What is the definition of a triangle?

Back

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Front

What is the relationship between the sides of a triangle and its angles?

Back

In a triangle, the larger the angle, the longer the opposite side. This is known as the angle-side relationship.

Front

What is the significance of the inradius in a triangle?

Back

The inradius is the radius of the inscribed circle of the triangle, which touches all three sides. It is important for calculating the area of the triangle.

Front

How do you find the area of a triangle using the inradius?

Back

The area (A) of a triangle can be calculated using the formula: A = r * s, where r is the inradius and s is the semi-perimeter.