Question

In the adjoining figure, AD = BC and AB is the perpendicular.
Show that CD bisects AB.​

Answer 1

${ \underline{ \underline{ \large{ \color{blue}{ {\mathtt{Correct \: \: question:- }}}}}}}$

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

$\huge \huge\bold\color{blue}{\underbrace{\overbrace{\mathfrak{\color{red}{✍Answer⭐}}}}}$

Given :-

• AD = BC
• ∠OAD = ∠OBC = 90°

To prove :-

• OD = BC ( Show that CD bisects AB.)

In ∆BOC and ∆AOD,

》 BOC = AOD (Vertically opposite angles)

》 CBO = DAO (Each 90º)

》 BC = AD (Given)

By AAS congruence rule,

∴ ∆BOC≅ ∆AOD

By CPCT

》 BO = AO

Therefore, CD bisects AB because BO = AO.

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.

Plz mrk as brainliest ❤

Hope it helps ❤