Question

AD and BC are equal perpendiculars to a line
segment AB (see Fig. 7.18). Show that CD bisects
AB.​

Answer 1

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 ❤

Answer 2

$\huge\underline{\overline{\mid{\bold{\red{★ ᴀɴsᴡᴇʀ ★}}\mid}}}∣$

Given:

 AB and BC are equal, BC= AD

To Prove:

 CD bisects  AB

Proof:

 In ∆BOC and ∆AOD

∠BOC = ∠AOD( Vertically opposite angle))

∠CBO = ∠DAO (each 90°)

BC= AD (GIVEN)

∴ ∆BOC ≅ ∆AOD (AAS Congruence Rule)

⇒ OB = OA [By C.P.C.T.]

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

Thus, CD bisects AB.

Hence Proved