This pdf includes the following topics:- Midpoint Segment bisector The Midpoint Formula Bisecting an Angle
1. Chapter 1 Basics of Geometry
2. Section 5 Segment and Angle Bisectors
3. The __midpoint__ of a segment is the point that divides, or __bisects__, the segment into two congruent segments. In this book, matched red congruence marks identify congruent segments in diagrams. A __segment bisector__ is a segment, ray, line, or plane that intersects a segment at its midpoint. C A M B A M B D M is the midpoint of AB if M is on AB and AM = MB. CD is a bisector of AB.
4. You can use a compass and a straightedge (a ruler without marks) to construct a segment bisector and midpoint of AB. A construction is a geometric drawing that uses a limited set of tools, usually a compass and a straightedge.
5. If you know the coordinates of the endpoints of a segment, you can calculate the coordinates of the midpoint. You simply take the mean, or average, of the x-coordinates and of the y-coordinates. This methods is summarized as the Midpoint Formula.
6. The Midpoint Formula If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint of AB has coordinates x1 x 2 y1 y 2 , 2 2
7. Example 1: Finding the Coordinates of the Midpoint of a Segment Find the coordinates of the midpoint of AB with endpoints A(-2, 3) and B(5, -2).
8. Example 2: Finding the Coordinates of an Endpoint of a Segment ***TEST*** The midpoint of RP is M(2, 4). One endpoint is R(-1, 7). Find the coordinates of the other endpoint.
9. GOAL 2: Bisecting an Angle A An angle bisector is a ray that divides an angle into two adjacent angles that are D congruent. In the diagram at the right, the C ray CD bisects angle into two congruent angles, and In this book, matching congruence arcs identify congruent angles in diagrams.
10. Example 3: Dividing an Angle Measure in Half The ray FH bisects the angle m H F 120° 120/2 = 60 m m
11. Example 4: Doubling an Angle Measure K In the kite, two angles are bisected. 45° E I Find the measure of the two angles. m m
12. Example 5: Finding the Measure of an Angle In the diagram, RQ bisect of the two congruent angles are (x + 40)° and (3x – 20)°. Solve for x. (x + 40)° Q R (3x – 20)° S
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