Question

ad and bd are equal perpendiculars to a line segment ab. Show that cd bisects ab​

Answer 1

Answer:

Let the middle point be O

Given -

AD =BD

Angle A = Angle B (each 90°)

Angle DOA = Angle BOC (vertically opposite angles)

So by AAS we can say that both the triangles are congruent

And AO = BO

Step-by-step explanation:

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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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