Question

AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides if AB prove that CD bisects AB.

Answer 1

let the line CD cut AB in E. Triangles CAE and DBE are congruent because angle C eqls agle D (alternate) , angle A =angle B =90, AD and BC are equal. Hence AE=BE

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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