Question

examples of topic perpendicular angle bisectors plus explanation

Answer 1

Answer on Question#43055-Math-Geometry

Question

Examples of topic perpendicular and angle bisectors plus explanation

Answer

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. The most often considered types of bisectors are the perpendicular bisector and the angle bisector.

The perpendicular bisector is a line that passes through the midpoint of a given segment:

CD is a perpendicular bisector of segment AB. AD = DB

In the triangle ABC in figure below DP, EP and FP are examples of perpendicular bisectors of the triangle sides.

DQ is bisector of side AB (AD=DB), EQ is bisector of side BC (BE=EC) and FP is bisector of side AC (AF=FC).

The angle bisector is a line that passes through the apex of an angle that divides it into two equal angles:

AD is an angle bisector of the angle $\angle$ BAC. $\angle$ BAD = $\angle$ DAC

In the triangle ABC in figure below AQ, BQ and CQ are examples of angle bisectors of a triangle.

AQ is bisector of $\angle$ CAB ( $\angle$ CAQ = $\angle$ QAB), BQ is bisector of $\angle$ ABC ( $\angle$ ABQ = $\angle$ QBC) and CQ is bisector of $\angle$ BCA ( $\angle$ BCQ = $\angle$ QCA).

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