Today I am solving the ncert class 9th solution of chapter triangles.Find the best solution of exercise 7.1 question number 3, also find the simplest and easiest solution of this question. Please help me to solve this in a simplest method. AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.
Solution:
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
Now,
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.
So, AO = OB (by the rule of CPCT).
Thus, CD bisects AB (Hence proved).