D is a point on side BC of ΔABC such that ∠ABC > ∠ACB and AB > AD. Then, which of the following statement is always true?
A)∠ACB > ∠ADC
B)∠ABC > ∠ADC
C)∠ACB < ∠ADC
D)∠ADB < ∠ABC
need explanation
I have no points left with me pls answer I have post this last time .
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If D is a point on the side AB of △ ABC such that AD : DB = 3:2 and E is a point on BC such that DE ∥ AC. Find the ratio of areas of △ ABC and △ BDE.
Answer:
Answer
DB
AD
=
2
3
[ Given ]
∴
DB
AD
+1=
2
3
+1
∴
DB
AD+DB
=
2
3+2
∴
DB
AB
=
2
5
--- ( 1 )
In △BDE and △ABC
∠B=∠B [ Common ]
∠BAC=∠BDE [ ∵DE∥AC ]
∴ △ABC∼△BDE [ By AA similarity criteria ]
ar(△BDE)
ar(△ABC)
=
DB
2
AB
2
=
2
2
5
2
=
4
25
[ From ( 1 ) ]
∴ ar(△ABC):ar(△BDE)=25:4
solution
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