Question

in the adjoining figure ad =bc and ab is the perpendicular. show that cd bisects ab.

Answer 1

Step-by-step explanation:

In triangle AOD and triangle COB

Angle COB = angle AOD ( VOA)

Angle A = Angle B (given)

AD = BC ( given)

Therefore , By AAS property ,  the Two triangles are congruent

Hence By CPCT , AO = BO

=> CD bisects AB.

Answer 2

Question :-

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

Answer :-

In ∆BOC and ∆AOD, we have

∠BOC = ∠AOD  

BC = AD [Given]

∠BOC = ∠AOD [Vertically opposite angles]

∴ ∆OBC ≅ ∆OAD [By AAS congruency]

⇒ OB = OA [By C.P.C.T.]

i.e., O is the mid-point of AB.

Thus, CD bisects AB.

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