Understanding Perpendicular Bisectors in Triangles

This video tutorial explains how to solve for unknown values using the properties of perpendicular bisectors in triangles. It covers two examples: one for finding x and another for finding y, using congruence and perpendicularity properties. A special case is also discussed where the bisector passes through the opposite vertex, demonstrating the equal distance property of points on the bisector.

What property of a perpendicular bisector is used to determine the angle it forms with the side of a triangle?

• It is parallel to the side.

• It forms a 45-degree angle.

• It is perpendicular, forming a 90-degree angle.

• It bisects the angle at the vertex.

In the first example, what equation is set up to solve for x?

• x - 6 = 90

• 2x = 90

• 2x + 6 = 90

• x + 6 = 90

How is the length of the segment determined in the first example?

• By adding the lengths of two segments.

• By doubling the given length.

• By subtracting from the total length.

• By dividing the total length by two.

What is the value of y in the first example?

• 10

• 9

• 8

• 7

What equation is used to solve for y in the first example?

• y + 1 = 23

• 3y - 1 = 23

• 3y + 1 = 23

• y - 1 = 23

In the second example, what makes the problem a special case?

• The bisector is parallel to the base.

• The bisector is shorter than the side.

• The bisector passes through the opposite vertex.

• The bisector is longer than the side.

What property of the perpendicular bisector is highlighted in the second example?

• It is equidistant from the endpoints of the segment.

• It is always parallel to the base.

• It forms a 45-degree angle with the base.

• It divides the triangle into two equal areas.

What equation is set up to solve for x in the second example?

• x - 1 = 45

• 2x = 45

• x + 1 = 45

• 2x + 1 = 45

What is the value of x in the second example?

• 21

• 23

• 20

• 22

What is the main takeaway from the video?

• Perpendicular bisectors are not useful in geometry.

• Perpendicular bisectors can be used to find unknown values in triangles.

• Perpendicular bisectors are always longer than the sides.

• Perpendicular bisectors are only applicable to right triangles.