Introduction to Geometry: Parallel and Perpendicular Lines

think icon 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, segment AF is the perpendicular bisector of segment BD, AD = 15, and BD = 10. Find AB + BF.

figure with segment BD and perpendicular bisector AF, a segment connects A to D, a segment connects A to B
 

AB = AD
AB = 15

BF = (1/2)BD
BF = 5

AB + BF = 15 + 5 = 20
 
In the figure below, segment AF is the perpendicular-bisector of segment DN. What is
mangleCDA?

figure with segment DN and perpendicular bisector AF, a segment connects A to N, making a sixty-five degree angle, a segment connects A to D and continues to T, segment DN extends past D to point C
 

The measure of angle ADF equals the measure of angle ANF, so the measure of ADF also equals 65 degrees. Angle CDA and angle ADF are supplementary, so the measure of angle CDA must equal 115 degrees.