Notifications
Clear all
Triangles
1
Posts
2
Users
0
Likes
225
Views
0
11/07/2021 11:42 am
Topic starter
AD and BC are equal perpendiculars to a line segment AB (see Fig.). Show that CD bisects AB.
1 Answer
0
11/07/2021 11:43 am
It is given that AD and BC are two equal perpendiculars to AB.
We will have to prove that CD is the bisector of AB
Triangles ΔAOD and ΔBOC are similar by AAS congruency since,
(i) A = B (They are perpendiculars)
(ii) AD = BC (As given in the question)
(iii) AOD = BOC (They are vertically opposite angles)
∴ ΔAOD ΔBOC.
AO = OB (by the rule of CPCT).
Thus, CD bisects AB (Hence proved).