Bisector is a term you may encounter in GRE geometry problems. So what the heck is a bisector and how do you use conquer bisector problems on the GRE?
Bisection is the division of something into two equal or congruent parts, usually by a line or a ray, which is then called a bisector. When a bisector, bisects an angle, it divides the angle into two equal parts. In the following figure, is bisected by such that or in other words the angles are equal. is also referred as the angle bisector of .
GRE problems can become somewhat more complicated when the ray divided an angle into a specific ratio. In such cases you need to apply little bit of algebra to the underlying geometry concept.
Let’s look at an example problem so that this concept is clear in your mind:
In the above figure, splits the angle in such a way that the measure of angle and are in the ratio 2:3. What is the measure of angle ?
Step 1: We know that the sum of the interior angles is equal to the exterior angle. Therefore
From the figure we see that angle is a right angle. It follows that
Step 2: Since the measure of angle and are in the ratio 2:3, we can write and