Geometry 5-2 Bisectors in Triangles. Class Needs Straight Edge Patty Paper ( 1 now, 2 later) Compass Printer paper.

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Presentation transcript:

Geometry 5-2 Bisectors in Triangles

Class Needs Straight Edge Patty Paper ( 1 now, 2 later) Compass Printer paper

Investigation Finding a right bisector the easy way

Investigation Fold your patty paper so that endpoint P and Q land exactly on top of each other, that is, the coincide. Crease your paper along the fold

Investigation Unfold your paper. Draw a line in the crease. What is the relationship of this line to PQ? Use your ruler and protractor to verify your observations.

Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

Converse - Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

Investigation On patty paper, draw a large-scale angle. Label it PQR

Investigation

Place a point on your angle bisector. Label it A. Compare the distances from A to each of the two sides. Remember that “distance” means the shortest distance. Try it with other points on the angle bisector.

Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the sides of the angle

Converse - Angle Bisector Theorem If a point is the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

Practice Construction of a midsegment

Practice Construction of a Perpendicular Bisector

Practice Construction of an Angle Bisector

Practice Construction of an altitude

Practice

Homework Pages 251 – 254 9, 12 – 16, 18, 19, 56, 57