Loci — Part 2: Angle bisectors, midlines and combined loci: visual lesson, ICSE Class 10 Mathematics

Lesson

Loci, Part 2

Two lines that cross have two angle bisectors, and every point on them is equally far from both lines. Combining loci lets us locate points that obey two rules at once.

In this lesson you will

Draw the angle bisector and use it as the locus of points equidistant from two intersecting lines
Draw the locus of points equidistant from two parallel lines
Find a point that satisfies two conditions as the intersection of two loci, and count the solutions
Solve construction problems: construct, draw the loci, mark the points and measure

Every point of the bisector $b$ is the same distance from the two lines $p$ and $q$.

Concept

What you will be able to do

Draw the angle bisector and use it as a locus
Find the locus between two parallel lines
Locate points by intersecting two loci
Solve a construction problem and measure the answer

Concept

Locus 4: equidistant from two intersecting lines

The points equally far from two lines that cross at $O$ lie on the bisectors of the angles between them. Every point of a bisector is the same distance from the two lines.

distance to each line is measured at a right angle

\text{point on a bisector} \Rightarrow \text{distance to } p = \text{distance to } q

Every point of the bisector $b$ is the same distance from the two lines $p$ and $q$.

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