Exploring Angle and Side Relationships in Triangles

The video tutorial covers angle-side relationships in triangles, focusing on a bi-conditional theorem that relates side lengths to opposite angles. It explains how to apply this theorem to determine the largest and smallest angles and sides in a triangle. The tutorial also introduces the triangle inequality theorem, which states that the sum of any two sides must be greater than the third side to form a triangle. The video includes examples and exercises to practice solving inequalities and determining possible side lengths for triangle formation.

What does the bi-conditional theorem state about the relationship between side lengths and angles in a triangle?

• The smallest side is opposite the medium angle.

• The largest side is opposite the largest angle.

• The smallest side is opposite the largest angle.

• The largest side is opposite the smallest angle.

If side AB is the largest in a triangle, which angle is the largest?

• Angle B

• Angle D

• Angle A

• Angle C

In a triangle, if angle C is the smallest, which side is the smallest?

• Side CD

• Side AC

• Side BC

• Side AB

Given a triangle with angles 44°, 60°, and 82°, which side is the largest?

• All sides are equal

• Side opposite 82°

• Side opposite 60°

• Side opposite 44°

If two sides of a triangle are congruent, what can be said about the angles opposite these sides?

• They are supplementary.

• They are complementary.

• One is larger than the other.

• They are congruent.

What must be true for three side lengths to form a triangle?

• The sum of all three sides must be equal.

• The sum of any two sides must be less than the third side.

• The sum of any two sides must be equal to the third side.

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

If you have side lengths 3, 5, and 7, can they form a triangle?

• No, because 5 + 7 < 3

• Yes, because 3 + 5 > 7

• No, because 3 + 5 < 7

• Yes, because 3 + 7 > 5

For side lengths 4, 6, and 11, why can't they form a triangle?

• Because 4 + 6 < 11

• Because 6 + 11 > 4

• Because 4 + 6 > 11

• Because 4 + 11 > 6

If given two side lengths of 4 and 10, what is the possible range for the third side length?

• Between 4 and 10

• Between 10 and 20

• Between 6 and 14

• Between 1 and 14

When solving for x in the inequality 3x + 4x > x + 8, what is the solution?

• x > 2

• x > 3

• x > 5

• x > 4