Lesson 2: Triangle Inequalities

Question 1

This theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Answer 1

Triangle Inequality Theorem

Question 2

What happens if the sum of two sides is less than or equal to the third side?

Answer 2

A triangle cannot be formed.

Question 3

What is the mathematical expression for the Triangle Inequality Theorem?

Answer 3

If a, b, and c are the sides of a triangle, then a + b > c, a + c > b, and b + c > a.

Question 4

This theorem states that if one angle is larger than another, then the side opposite the larger angle is the longest side.

Answer 4

Side-Angle Theorem

Question 5

According to the Side-Angle Theorem, what happens when one angle is smaller than another?

Answer 5

The side opposite the smaller angle is the shortest side.

Question 6

This theorem states that if one side is larger than another, then the angle opposite the larger side is the largest angle.

Answer 6

Angle-Side Theorem

Question 7

According to the Angle-Side Theorem, what happens when one side is shorter than another?

Answer 7

The angle opposite the shorter side is the smallest angle.

Question 8

In a triangle, the longest side is always opposite this.

Answer 8

The largest angle

Question 9

In a triangle, the shortest side is always opposite this.

Answer 9

The smallest angle

Question 10

How should the sides of a triangle be arranged based on their lengths?

Answer 10

From shortest to longest

Question 11

How should the angles of a triangle be arranged based on their measures?

Answer 11

From smallest to largest

Question 12

Given Angle Missing; Sides

Answer 12

Angle-Side Inequality Theorem

Question 13

Given Sides Missing; Angles

Answer 13

Side-Angle Inequality Theorem