4. In an isosceles triangle ABC, AB = AC. Prove that the median AD, which meets BC at D is also the
perpendicular bisector of BC.
5. In the given figure, AB =DC and <ABC = <DCB. Prove that
(a) ∆ABC congruent to ∆DBC
(b) <A = <D
(c) ∆AOB congruent to ∆DOC
(d) ∆OBC is isosceles.
Attachments:
Answers
Answered by
46
Step-by-step explanation:
Ans4.In isosceles Triangle ABC
AB= AC [given]
Property of isosceles triangle.
AD = AD [ common]
Thus
Thus BD= CD [BY CPCT]
By CPCT
Now to prove that AD is a perpendicular bisector of BC,we have to prove with the help of linear pair
Hence proved.
Ans 5.
(a) ∆ABC ≈ ∆DBC
AB = DC [Given]
BC = BC [common]
By AAS CRITERION OF CONGRUENCY OF TRIANGLE ,
(ii) If two triangles are congruent than corresponding parts are equal, thus
by CPCT.
(iii) In ∆ AOB and ∆DOC
Thus by AAS CRITERION OF CONGRUENCY OF TRIANGLES,
(iv) Since ∆AOB and ∆ DOC are congruent,so
BO= CO (BY CPCT)
Thus ∆OBC is Isosceles.
Hope it helps you.
Attachments:
Answered by
7
in triangle abc ab=AC so angle a=angle b so using congruence prove bc=dc
Similar questions