Question

AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.​

Answer 1

Step-by-step explanation:

Given,

AD and BC are perpendiculars of AB.

\mathbb{ TO \:BE \:SHOWN }TOBESHOWN :

CD bisects AB

∠BOC = ∠DOC ( ∴ Vertically opposite angles )

DA = BC

∠B = ∠A = 90°

So, by \bf{AAS}AAS congruence condition, ΔBOC ≅ ΔOAD

So,

now CO = OD

so, it bisects AB on point '\bf{O}O '

OA = OB

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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