Question

3.
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.

:

CD bisects AB

∠BOC = ∠DOC ( ∴ Vertically opposite angles )

DA = BC

∠B = ∠A = 90°

So, by  congruence condition, ΔBOC ≅ ΔOAD

So,

now CO = OD

so, it bisects AB on point ''

OA = OB [ by  ]

➖➖➖➖➖➖➖➖➖➖➖➖➖

: Angle-Angle-side

: Corresponding Parts of Congruent Triangles

hope it helps you

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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