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This text explores the concept of perpendicular bisectors and angle bisectors in geometry through clear examples. It demonstrates how to bisect a line segment, such as linking points A and B, creating a perpendicular bisector that is a locus of all points equidistant from A and B. It also examines how to bisect an angle, illustrating the process with points A, B, and C, resulting in a line that equidistantly divides the angle. Additionally, procedures for dropping perpendiculars from points to lines are explained, enhancing understanding of geometric constructions.
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Constructions A Perpendicular bisector of a line Example Bisect the line joining A and B B
Example Bisect the line PQ Q P The line drawn is also known as a locus of all points which are equidistant (equal in distance) from P and Q.
2. Bisecting an angle Example Bisect the angle given by A A
Example Bisect the angle given by ABC C A B The line drawn is also known as a locus of all points which are equidistant (equal in distance) from AB and BC
3. Dropping a perpendicular from a point to a line Example Drop a perpendicular from the point P to the line AB P A B
Example Drop a perpendicular from the point P to the line LM L P M
