If side AB is longer than side AC in triangle ABC, which angle is greater?

Angle ACB is greater than angle B.

True or False: In any triangle, the sum of the lengths of any two sides is always less than the length of the third side.

False. The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Riddle: I am a type of angle that, when formed with a line, creates the shortest distance to that line. What am I?

Perpendicular angle.

Fill in the blanks: The difference between any two sides of a triangle is always ______ than the third side.

Less

Which theorem states that if two angles of a triangle are unequal, the greater angle has the greater side opposite to it?

The Converse of Theorem 3.

In triangle ACD, if AC equals AD, what can be said about angles ACD and ADC?

Angle ACD equals angle ADC.

True or False: In triangle ABC, if AB = AC, then angles B and C are equal.

True.

What is the relationship between the lengths of sides AB, AC, and BC in triangle ABC if AB is the longest side?

AB + AC > BC.

Riddle: I am the line segment from a point to a line, ensuring the shortest distance. What am I?

The perpendicular from the point to the line.

Fill in the blanks: The sum of the lengths of sides AB and AC must be greater than ______.

BC

In triangle ABC, if BP is a median, what is the relationship between PB + PA and BC + AC?

PB + PA < bc="" +="" />

What does the statement 'Of all lines drawn from a point outside a given line, the perpendicular is the shortest' imply?

The perpendicular line from the point to the line is the shortest distance.

True or False: The angles opposite equal sides of a triangle are always unequal.

False. The angles opposite equal sides of a triangle are equal.

Which construction is used to prove that angle ACB is greater than angle B in triangle ABC?

Cut off a segment AD equal to AC from side AB.

Riddle: I am a triangle property that sums two sides but must always exceed the measure of the third. What am I?

Triangle inequality.

Fill in the blanks: The exterior angle of a triangle is always ______ than either of the opposite interior angles.

Greater

If two sides of triangle ACD are equal, what can be said about the angles opposite those sides?

The angles opposite those sides are equal.

Which theorem states that if two sides of a triangle are unequal, the greater side has the greater angle opposite to it?

Theorem 3.

True or False: In triangle ABC, if angle A is the largest angle, then side BC is the shortest side.

True.

What is the conclusion if AD bisects angle BAC in triangle ABC?

AB > BD and AC > CD.