Question

AD and BC are equal and perpendicular to a line segment AB show that CD bisects AB​

Answer 1

Answer:

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Step-by-step explanation:

Triangles chapter Ncert book lesson 7

Answer 2

⇴Question :-

AD and BC are equal and perpendicular to a line segment AB show that CD bisects AB

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⇴Given :-

$\sf \: ad = bc.....(1) \\ \sf \: ad \perp \: ab \: i.e \: \angle \: oad = 90 \degree \: \\ \sf \: ac \perp \: ab \: i.e \: \angle \: obc \: = 90 \degree \:$

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⇴ To prove :-

CD bisects AB i.e . OA = OB

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⇴Proof :-

since , line CD & AB intersects

angle AOD = angle BOC (vertically opposite angles)

In , ∆BOC & ∆ AOD

$\sf \: \angle \: boc \: = \angle \: aod \: (from(2)) \\ \sf \angle \: cbo = \angle \: dao \: (both \: angles \: are \: 90 \degree$

BC = AD (from 1)

⇴therefore ,

$\sf \: \triangle \: boc \: \cong \: \triangle \: aod \: (aas \: congruency \: ) \\ \bf \: \therefore \: bo = ao \: (cpct)$

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