Question

AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

Answer 1

angle ADC= angle OCB
side AD=side BC
angle OAD=angle OBC
By A-S-A test
∆OAD≈∆OBC
Therefore
OB=OA
therefore CO bisects AB
since C,O,D are collinear
CD bisects AB
hence proved

Answer 2

Answer:

Step-by-step explanation:

angle ADC= angle OCB

side AD=side BC

angle OAD=angle OBC

By A-S-A test  

∆OAD≈∆OBC

Therefore  

OB=OA  

therefore CO bisects AB

since C,O,D are collinear  

CD bisects AB  

hence proved