**AD and BC are equal perpendiculars to a line segment AB (see Figure). Show that CD bisects AB.**

**Solution:**

In and .

, But these are alternate interior angles. It means that .

** (Alternate Interior Angles, )**

BC=AD ** (Given)**

**(Given)**

Therefore, by ASA rule, we have

Hence, BO=AO **(Corresponding Parts of Congruent Triangles)**

**It means that CD bisects AB.**