5.2 Use Perpendicular Bisectors - Mr. Kuhlthau's...
Transcript of 5.2 Use Perpendicular Bisectors - Mr. Kuhlthau's...
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5.2 Use Perpendicular Bisectors
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A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector
Theorem 5.2 Perpendicular Bisector Theorem:
In a plane, if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
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In the diagram line ZX is the perpendicular bisector of line WY.
• Find WZ • Find XY
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Theorem 5.3 Converse of the Perpendicular Bisector Theorem:
In a plane, if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
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ACTIVITY TIME: Fold the perpendicular bisectors of a triangle
Question to ponder: Where do the perpendicular bisectors of a triangle meet?
Step 1: Cut a large acute scalene triangle out of paper.
Step 2: Fold the triangle to form the perpendicular bisectors of the sides. Do the three perpendicular bisectors intersect at the same point?
Concurrent: 3 or more lines, rays, or segments that intersect at the same point
Point of Concurrency: the point of intersection of 3 or more lines, rays, or segments
Circumcenter: the point of concurrency of the 3 perpendicular bisectors of a triangle
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Note where the circumcenter lies in the different triangles: acute, right, obtuse
(We are focusing on the acute triangle with this activity)
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Step 3: Label the vertices A, B, and C. Label the point of intersection of the perpendicular bisectors as P. Measure AP, BP, and CP. What do you observe?
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Circumcenter: the point of concurrency of the 3 perpendicular bisectors of a triangle
Theorem 5.4 Concurrency of Perpendicular Bisectors of a Triangle:
The perpendicular bisectors of a triangle intersect at a point (the circumcenter) that is equidistant from the vertices of the triangle.
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The perpendicular bisectors of ∆ABC meet at point G. Find GB
The perpendicular bisectors of ∆RST meet at point D. Find DR.
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For the rest of class, complete the worksheet and handin:
5.2 Practice B
Take out your student handbook and write down the homework assignment:
5.1 and 5.2 Quiz Review