Understanding the Angle-Side Theorem and Its Applications

The video tutorial covers the angle side theorem, also known as the base angle theorem, which states that if two sides of a triangle are congruent, then the angles opposite those sides are congruent. The converse is also true. The video provides examples and problems to illustrate these concepts, including solving for unknown angles and using inequalities in triangles. It also demonstrates how to apply the theorem in two column proofs, emphasizing the relationship between congruent sides and angles in triangles.

What does the Angle-Side Theorem state about the relationship between sides and angles in a triangle?

• If two sides are congruent, the angles opposite them are congruent.

• If two angles are congruent, the sides adjacent to them are congruent.

• If two sides are congruent, the angles adjacent to them are congruent.

• If two angles are congruent, the sides opposite them are not congruent.

In the converse of the Angle-Side Theorem, what is true if two angles of a triangle are congruent?

• The triangle is equilateral.

• The sides opposite those angles are congruent.

• The sides adjacent to those angles are congruent.

• The triangle is isosceles.

If angle A is 30 degrees and angle C is also 30 degrees in triangle ABC, what can be said about sides AB and BC?

• AB is not related to BC.

• AB is longer than BC.

• AB is congruent to BC.

• AB is shorter than BC.

In a scalene triangle, if side AB is 11 and side BC is 12, which angle is larger?

• Angle A and C are equal

• Angle B

• Angle A

• Angle C

What is the relationship between the longest side and the largest angle in a triangle?

• The longest side is not related to the angles.

• The longest side is adjacent to the largest angle.

• The longest side is opposite the largest angle.

• The longest side is opposite the smallest angle.

If angle A is greater than angle C in a triangle, what can be said about sides BC and AB?

• BC is shorter than AB.

• BC is not related to AB.

• BC is longer than AB.

• BC is equal to AB.

What is the maximum value of x if angle A is 9x - 16 and angle C is 5x + 8, given that angle A is greater than angle C?

• x < 15

• x < 10

• x < 13.4

• x < 6

In a two-column proof, what is the reason for stating that two triangles are congruent if two sides and the included angle are congruent?

• Angle-Side-Angle Postulate

• Angle-Angle-Side Postulate

• Side-Side-Side Postulate

• Side-Angle-Side Postulate

What is the reason for concluding that angle 1 is congruent to angle 4 if they are supplements of congruent angles?

• Base Angles Theorem

• Vertical Angles Theorem

• Congruent Supplements Theorem

• Supplementary Angles Theorem

In a two-column proof, what is the reason for stating that corresponding parts of congruent triangles are congruent?

• CPCTC

• SAS

• ASA

• SSS