Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the triangle inequality theorem, explaining how a triangle can exist if the sum of its two smaller sides is greater than the third side. It provides examples to determine if given side lengths can form a triangle using inequalities. The tutorial also discusses how to set up inequalities to find the range of possible lengths for a triangle's third side. Additionally, it explains how to order angles by comparing side lengths and vice versa, using color-coding for better understanding.

Can the side lengths 8, 17, and 24 form a triangle?

• Yes

• No

• Only if it's a right triangle

• Insufficient information

What is the Triangle Inequality Theorem primarily about?

• The sum of any two angles of a triangle must be less than 180 degrees.

• The sum of any two sides of a triangle must be greater than the third side.

• The sum of any two sides of a triangle is equal to the third side.

• The longest side of a triangle is always twice the length of the shortest side.

If a triangle has sides of lengths 11 and 3, what is the range of the third side?

• Between 10 and 12

• Between 9 and 13

• Between 8 and 14

• Between 7 and 15

What is the range of possible lengths for the third side if two sides of a triangle are 14 and 22?

• Between 8 and 36

• Between 7 and 37

• Between 9 and 35

• Between 6 and 38

Which angle is the largest when side lengths are 7, 9, and 13?

• Angle opposite side 13

• Angle opposite side 9

• Angle opposite side 7

• All angles are equal

How are the angles of a triangle ordered in relation to the sides?

• Largest angle opposite the shortest side

• Smallest angle opposite the shortest side

• Smallest angle opposite the longest side

• Angles and sides are not related

For a triangle with angles measuring 103 and 42 degrees, what is the length of the smallest side?

• Cannot be determined

• Opposite the 35-degree angle

• Opposite the 103-degree angle

• Opposite the 42-degree angle

If two angles of a triangle are 57 and 31 degrees, which side is the longest?

• Opposite the 92-degree angle

• All sides are equal

• Opposite the 31-degree angle

• Opposite the 57-degree angle

What is the missing angle in a triangle if two angles measure 82 and 54 degrees?

• 48 degrees

• None of the above

• 36 degrees

• 44 degrees

In a triangle with sides labeled X, Y, and Z, if angle X is the smallest, which side is the longest?

• Side Y

• Cannot be determined from the given information

• Side Z

• Opposite angle X