Properties of Angles and Rays

This video tutorial covers the transitive and substitution properties, as well as vertical angles. It explains how angles congruent to the same angle are congruent to each other (transitive property) and how one variable can be replaced with another (substitution property). The video also discusses vertical angles formed by intersecting lines, highlighting their congruence and supplementary nature. An example problem is solved to demonstrate these concepts in practice.

What does the transitive property state about angles?

• If two angles are supplementary, they are congruent.

• If two angles are congruent to a third angle, they are congruent to each other.

• If two angles are vertical, they are congruent.

• If two angles are adjacent, they are congruent.

How does the substitution property work?

• By replacing one angle with another to show congruence.

• By multiplying two angles together.

• By adding two angles to find a third angle.

• By subtracting one angle from another.

Which property involves linking two equations to form a new equation?

• Opposite Rays Property

• Vertical Angles Property

• Transitive Property

• Substitution Property

Which of the following is true about vertical angles?

• They are always complementary.

• They are always supplementary.

• They are always congruent.

• They are always adjacent.

What is the sum of angles 2 and 3 if they form a linear pair?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

What are opposite rays?

• Two rays that form a right angle.

• Two rays that form a linear pair.

• Two rays that extend in the same direction.

• Two collinear rays with a common endpoint extending in opposite directions.

In the example problem, what is the measure of angle 2 when x equals 8?

• 90 degrees

• 80 degrees

• 70 degrees

• 60 degrees

What is the measure of angle 2 when x equals -1 in the example problem?

• 5 degrees

• 6 degrees

• 8 degrees

• 7 degrees

What is the relationship between angles 2 and 3 in the example problem?

• They are adjacent.

• They are supplementary.

• They are congruent.

• They are complementary.

What is the result of substituting angle 3 with 7x + 14 in the example problem?

• x plus 1

• 7x plus 14

• x squared plus 6

• x minus 8