Math, asked by brainlybunny, 4 months ago


5. In the given figure, AB = DC and angleABC = angleDCB. Prove that
(a) ∆ABC = ∆DCB
(b) angleA = angleD
(c) ∆AOB = ∆DOC
(d) ∆OBC is isosceles
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Answered by Anonymous
1

\huge\underline\bold\red{Correct Question}

In the given figure, AB = DC and ∠BC = ∠DCB. Prove that

(a) ∆ABC = ∆DCB

(b) ∠A = ∠D

(c) ∆AQB = ∆DQC

(d) ∆QBC is isosceles

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\huge\underline\bold\red{Answer }

∆ABC & ∆DCB :-

  • AB = DC
  • ∠ABC = ∠DCB
  • BC = same base

Therefore proved ∆ABC = ∆DCB [ SAS criterion ]

★ ∠A = ∠D

Since BC is the same base for both the angles and according to the theorem angles on the same base is equal

★ Proof :-

  • ∠AQB = ∠DQC
  • AB = DC
  • ∠BAC = ∠BDC

∆AQB = ∆DQC

BQ = QC [ CPCTC ]

★ As, BQ = QC [ proved above ]

So, ∆OBC is an isosceles triangle

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