Exploring Perpendicular and Angle Bisectors in Geometry

This video lesson covers section 5.1 of CP Geometry, focusing on perpendicular and angle bisectors in triangles. It explains the properties of perpendicular bisectors, including their ability to create right angles and divide sides into congruent segments. The lesson also discusses special cases where perpendicular bisectors originate from a vertex, leading to angle bisection. Practical examples are provided to apply these concepts, followed by an introduction to angle bisectors, which originate at an angle and divide it into two equal parts. The video concludes with practical examples and a summary of key points.

What is the primary function of a perpendicular bisector in a triangle?

• To divide an angle into two equal parts

• To create a right angle with a side and divide it into two equal parts

• To connect two vertices of a triangle

• To divide the triangle into two congruent triangles

When does a perpendicular bisector also bisect the angle in a triangle?

• When it is parallel to one of the sides

• When it originates from the midpoint of a side

• When it is the longest side of the triangle

• When it originates from a vertex

In the given problem, if AC is perpendicular to BD and originates from a vertex, what additional property does it have?

• It bisects the opposite side into two equal parts

• It also bisects the angle at the vertex

• It creates two right angles at the base

• It divides the triangle into two isosceles triangles

How do you determine the perimeter of a triangle when given a perpendicular bisector that bisects one of its sides?

• By adding the lengths of all sides directly

• By finding the length of the bisector and doubling it

• By measuring the angles and using trigonometry

• By using the properties of congruent triangles formed by the bisector

What is the key difference between an angle bisector and a perpendicular bisector?

• A perpendicular bisector does not create right angles

• An angle bisector divides an angle into two equal parts

• A perpendicular bisector always originates from a vertex

• An angle bisector divides a side into two equal parts

Which of the following is true about angle bisectors in a triangle?

• They always divide the opposite side into two equal parts

• They always create right angles with the sides

• They originate from an angle and divide it into two equal parts

• They are always perpendicular to one of the sides

In the example with angle bisectors, why are the two triangles congruent?

• Because they share a common side and have two equal angles

• Because they are both right triangles

• Because they have the same area

• Because they have the same perimeter

What theorem is used to determine that corresponding parts of congruent triangles are congruent?

• Triangle Inequality Theorem

• Angle Sum Theorem

• Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

• Pythagorean Theorem

If an angle bisector divides an angle into two 52-degree angles, what is the measure of the original angle?

• 90 degrees

• 52 degrees

• 104 degrees

• 180 degrees

What type of triangle is formed when a perpendicular bisector also bisects the angle at the vertex?

• Right triangle

• Isosceles triangle

• Equilateral triangle

• Scalene triangle