This video tutorial explains how to solve for unknown values using the properties of perpendicular bisectors in triangles. It covers two examples: one for solving x and another for solving y, using the concept of segment congruence. A special case is also discussed where the perpendicular bisector passes through the opposite vertex, demonstrating that any point on the bisector is equidistant from the segment's endpoints. The video concludes with a verification of the solutions.

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

• It is perpendicular to a side and bisects it.

• It always passes through the centroid.

• It is parallel to one side of the triangle.

• It divides the triangle into two equal areas.

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CCSS.7.G.B.5

In the first example, what equation is set up to find the value of x?

• 2x - 6 = 90

• x + 6 = 90

• 2x + 6 = 90

• x - 6 = 90

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CCSS.8.G.A.5

What is the value of x in the first example?

• 43

• 44

• 41

• 42

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CCSS.4.MD.A.2

How is the value of y determined in the first example?

• By setting 3y - 1 equal to 23

• By setting 3y - 1 equal to 46

• By setting y - 1 equal to 23

• By setting 3y + 1 equal to 23

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CCSS.8.G.B.8

What is the value of y in the first example?

• 6

• 7

• 8

• 9

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CCSS.HSG.CO.C.9

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

• The bisector is parallel to the base.

• The bisector is not perpendicular.

• The bisector passes through the opposite vertex.

• The bisector passes through the centroid.

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CCSS.4.MD.A.2

What equation is used to find x in the second example?

• 2x + 1 = 45

• 2x - 1 = 45

• x + 1 = 45

• x - 1 = 45

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CCSS.8.G.A.5

What is the value of x in the second example?

• 20

• 21

• 23

• 22

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CCSS.HSG.CO.C.9

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

• It is parallel to one side of the triangle.

• It always passes through the centroid.

• Any point on it is equidistant from the endpoints of the segment it bisects.

• It divides the triangle into two equal areas.

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CCSS.HSG.C.A.3

What is the main takeaway from the video?

• Perpendicular bisectors always pass through the centroid.

• Perpendicular bisectors divide the triangle into two equal areas.

• Perpendicular bisectors are always parallel to the base.

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

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CCSS.HSG.C.A.3