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Question

ABC and DBC are two iosceles triangle on the same base BC and vertices A and D are on the same sides of BC. If AD is exerted to intersect BC at P, show that
ABPtriangleACP
1363705_cdceec7ce1e24fe2bb9ae68b61ac45c8.png

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Solution

Given:ABC is isosceles, AB=AC ......(1)
Also,DBC is isosceles, DB=DC ......(2)
In ABC and DBC, we have
AB=AC from (1)
BD=DC from (2)
AD=AD(common)
ABDACD(SSS congruence rule)
So, BAP=PAC by CPCT ......(1)
In ABP and ACP,
AB=AC(given)
BAP=PAC from (1)
AP=AP(common)
ABPACP by SAS congruence rule.


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