Exploring Adding and Subtracting Rational Expressions

The video tutorial explores the properties of triangles, focusing on the angle sum theorem, which states that the sum of a triangle's angles is always 180 degrees. It includes a dynamic demonstration to visualize this concept. The tutorial also covers methods to find missing angles in triangles and explains the triangle inequality theorem, which determines if three sides can form a triangle. Finally, it discusses the relationship between angles and sides, emphasizing that the longest side is opposite the largest angle and vice versa.

What is the sum of the angles in any triangle?

• 270 degrees

• 90 degrees

• 180 degrees

• 360 degrees

If two angles in a triangle are 73 degrees and 41 degrees, what is the measure of the third angle?

• 96 degrees

• 86 degrees

• 76 degrees

• 66 degrees

What is the measure of the missing angle if the other two angles are 21 degrees and 126 degrees?

• 33 degrees

• 43 degrees

• 63 degrees

• 53 degrees

What is the sum of the lengths of the two shortest sides in a triangle compared to the length of the longest side?

• Greater than the longest side

• Less than the longest side

• Equal to the longest side

• Cannot be determined

Given sides of lengths 6.8, 7.2, and 5.1, will they form a triangle?

• No, because 5.1 is too short

• Yes, because 7.2 is the longest side

• No, because 6.8 + 5.1 < 7.2

• Yes, because 6.8 + 5.1 > 7.2

If the sides of a triangle are 3, 5, and 8, will they form a triangle?

• Yes, because 8 is the longest side

• No, because 3 + 5 = 8

• Yes, because 3 + 5 > 8

• No, because 3 + 8 > 5

Where is the longest side of a triangle located?

• Next to the smallest angle

• Opposite the largest angle

• Opposite the smallest angle

• Next to the largest angle

In a triangle, the shortest side is always located opposite which angle?

• The obtuse angle

• The largest angle

• The smallest angle

• The right angle

Given a triangle with sides 14.3, 15.7, and 12.1, which angle is the largest?

• The angle opposite 15.7

• The angle opposite 12.1

• The angle opposite 14.3

• Cannot be determined

If a triangle has angles of 45, 55, and 80 degrees, which side is the longest?

• The side opposite the 45-degree angle

• The side opposite the 55-degree angle

• The side opposite the 80-degree angle

• Cannot be determined