Understanding the Right Angle Theorem

The video tutorial covers the right angle theorem, explaining that if two angles are both supplementary and congruent, they are right angles. It demonstrates this concept through examples, including a two-column proof and proving a line is an altitude. The tutorial also includes solving algebraic equations to determine if lines are perpendicular.

What is the result when two angles are both supplementary and congruent?

• They are acute angles.

• They are obtuse angles.

• They are right angles.

• They are complementary angles.

What is the sum of angles in a linear pair?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

In the example of the two-column proof, what is the goal of the proof?

• To prove that point P is the center of the circle.

• To prove that two triangles are similar.

• To prove that segment PB is perpendicular to segment AC.

• To prove that two angles are complementary.

Which postulate is used to prove the congruence of triangles in the example?

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

Which property states that a segment is congruent to itself?

• Transitive Property

• Symmetric Property

• Substitution Property

• Reflexive Property

What is the definition of an altitude in a triangle?

• A segment from a vertex perpendicular to the opposite side.

• A segment that is parallel to the base.

• A segment that divides the triangle into two equal areas.

• A segment that bisects an angle.

What is the result when two lines intersect at right angles?

• They are skew.

• They are perpendicular.

• They are parallel.

• They are collinear.

What is the value of x when solving the system of equations to determine perpendicularity?

• 18

• 15

• 12

• 10

What is the value of y when solving the system of equations to determine perpendicularity?

• 15

• 18

• 12

• 10

What is the measure of each angle when x = 12 and y = 15 in the system of equations?

• 90 degrees

• 60 degrees

• 105 degrees

• 75 degrees