Question

5. In the given figure, AB = DC and angle ABC = DCB. Prove that
(a) angle ABC congruent angle DBC
(b) angle A = angle D
(c) angle AOB congruent angle DOC
(d) angle OBC is isosceles.
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Answer 1

Step-by-step explanation:

1) in ∆ ABC and ∆ DCB,

AB = DC [ given ]

angle ABC = angle DCB [ given ]

BC = BC [ common side ]

by SAS rule, ∆ ABC ~ ∆ DBC

2) by CPCT, angle A = angle D

3) in ∆ AOB and ∆ DOC,

angle A = angle D. [ proved above ]

angle AOB = angle DOC [ vertically opposite angles ]

AB = DC [ given ]

by AAS rule, ∆ AOB ~ ∆ DOC

4) since ∆ AOB ~ ∆ DOC, by cpct, OB = OC

hence ∆ OBC is an isosceles ∆

hence proved

Answer 2

Answer:

5(a) PROOF: In triangle ABC & triangle DBC

AB = DC (given)

angle ABC = angle DCB (given)

BC = BC (common)

hence, by SAS criteria

triangle ABC congruent triangle DCB..

(B) Ans- angle A = angle D ( c.p.c.t)

Q c & d I'll try later