Properties of Angles in Triangles

The video tutorial explains a geometric theorem stating that if one side of a triangle is longer than another, the angle opposite the longer side is greater. It uses an example triangle to illustrate this concept and then sets up a proof by creating an isosceles triangle. The proof involves using the base angles theorem and substitution to show that the measure of one angle is greater than another. The tutorial concludes by summarizing the proof and its implications.

What does the theorem state about the angles in a triangle when one side is longer than another?

• The angle opposite the longer side is equal.

• The angle opposite the longer side is smaller.

• The angles are unrelated to the side lengths.

• The angle opposite the longer side is greater.

In the given triangle example, which angle is opposite the longest side?

• None of the above

• Angle A

• Angle B

• Angle C

What is the purpose of selecting a point on side AC in the proof strategy?

• To create a right triangle

• To form an isosceles triangle

• To divide the triangle into two equal parts

• To make the triangle equilateral

What property of isosceles triangles is used in the proof?

• The angles are all 60 degrees

• The sides are all equal

• The base angles are congruent

• The triangle is right-angled

Which theorem is used to relate the exterior angle to the non-adjacent angles?

• Pythagorean Theorem

• Base Angles Theorem

• Angle Addition Postulate

• Exterior Angle Theorem

How is the measure of angle B expressed in terms of other angles in the proof?

• As the difference between angle three and angle C

• As the sum of angle three and angle one

• As twice the measure of angle C

• As the sum of angle one and angle C

Which property is used to substitute angle measures in the proof?

• Angle Addition Postulate

• Substitution Property

• Ruler Postulate

• Congruence Property

What conclusion is drawn about angle B compared to angle C?

• Angle B is smaller than angle C

• Angle B is unrelated to angle C

• Angle B is equal to angle C

• Angle B is greater than angle C

What is the final step in proving the theorem?

• Demonstrating angle B is greater than angle C

• Showing angle B is equal to angle C

• Proving angle B is less than angle C

• Concluding angle B is unrelated to angle C

What is the significance of adding the measure of angle three twice in the proof?

• It has no significance

• It proves angle B is greater

• It shows angle B is smaller

• It indicates angle B is equal