Introduction to Geometry: Parallel and Perpendicular Lines

Think & Click: Perpendicular Lines and Angle Bisectors

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

In the following figure, segments AB and CR are perpendicular, and DH is the bisector of angle ADC. Find m angle HDF. We will work through this step by step.

perpendicular segments A B and C R intersect and point D, angle F D R is 30 degrees and segment D H is the bisector of angle A D C

Since the segments are perpendicular, what can you say about m angle

ADC and m

ADR?

They both equal 90 degrees, since the lines are perpendicular.

Since segment DH is an angle bisector, find m angle

HDA.

It will equal half of 90 degrees. It equals 45 degrees.

Find m

ADF.

The measure of angle ADF plus 30 degrees will equal 90 degrees, since the lines are perpendicular. The measure of angle ADF equals 60 degrees.

Find m

HDF.

measure of angle H D F equals measure of angle H D A plus measure of angle A D F equals 45 degrees plus 60 degrees equals 105 degrees