Exploring the Triangle Inequality Theorem

In this video, Mr. Yanos introduces the triangle inequality theorem, explaining that a triangle exists if the sum of its two smaller sides is greater than the third side. He provides examples to illustrate this concept and demonstrates how to determine if given side lengths can form a triangle. The video also covers how to find possible values for a triangle's third side when only two sides are known. Additionally, Mr. Yanos explains how to order angles and sides based on their measures, using examples to clarify these concepts. The video concludes with practice problems to reinforce the material covered.

According to the triangle inequality theorem, a triangle exists if the sum of which sides is greater than the third side?

• The largest and smallest sides

• The two smallest sides

• Any two sides

• The two largest sides

Can the side lengths 2, 4, and 7 form a triangle?

• Yes, because 2 + 4 is greater than 7

• No, because 2 + 4 is not greater than 7

• No, because 4 + 7 is not greater than 2

• Yes, because 2 + 7 is greater than 4

If a triangle has sides of lengths 10 and 7, what is the minimum possible value for the third side?

• 3

• 7

• 10

• 17

If a triangle has sides of lengths 10 and 7, what is the maximum possible value for the third side?

• 3

• 17

• 10

• 7

In a triangle with sides 7, 13, and 10, which angle is opposite the shortest side?

• Angle D

• Angle A

• Angle B

• Angle C

In a triangle with sides 7, 13, and 10, which angle is opposite the longest side?

• Angle C

• Angle B

• Angle D

• Angle A

In a triangle with angles 35°, 42°, and 103°, which side is opposite the smallest angle?

• Side DF

• Side DE

• Side AC

• Side EF

In a triangle with angles 35°, 42°, and 103°, which side is opposite the largest angle?

• Side EF

• Side DF

• Side DE

• Side AC

Given a triangle with side lengths 8, 17, and 24, can these sides form a triangle?

• No, because 17 + 24 is not greater than 8

• Yes, because 8 + 17 is greater than 24

• Yes, because 8 + 24 is greater than 17

• No, because 8 + 17 is not greater than 24

Given a triangle with angles 59°, 68°, and 53°, which side is opposite the smallest angle?

• Side ST

• Side SV

• Side TV

• Side DE