5. In the adjoining figure, if AD/DC = BE/EC and angleCDE = angleCED Prove that triangleCAB is isosceles.
Standard:- 10th
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Hey!!!
Good Morning
Difficulty Level : Average
Chances of being asked in Board : 50%
______________
Given : ∆CAB in which AD/DC = BE/EC and
angle CDE = angle CED ------ (1)
To Prove : ∆CAB is isosceles
Proof : Here if AD/DC = BE/EC, by Converse of BPT,
=> DE II AB
Thus
=> angle CDE = angle A -------(2)
=> angle CED = Angle B -------(3)
From (1) , (2) and (3)
=> angle A = angle B
Thus
=> AC = BC (side opposite equal angles)
Thus ∆CAB is an isosceles triangle
Hence Proved
__________________
Hope this helps ✌️
Good Morning
Difficulty Level : Average
Chances of being asked in Board : 50%
______________
Given : ∆CAB in which AD/DC = BE/EC and
angle CDE = angle CED ------ (1)
To Prove : ∆CAB is isosceles
Proof : Here if AD/DC = BE/EC, by Converse of BPT,
=> DE II AB
Thus
=> angle CDE = angle A -------(2)
=> angle CED = Angle B -------(3)
From (1) , (2) and (3)
=> angle A = angle B
Thus
=> AC = BC (side opposite equal angles)
Thus ∆CAB is an isosceles triangle
Hence Proved
__________________
Hope this helps ✌️
Answered by
25
Answer:
Step-by-step explanation:
Given : ∆CAB in which AD/DC = BE/EC and
angle CDE = angle CED ------ (1)
To Prove : ∆CAB is isosceles
Proof : Here if AD/DC = BE/EC, by Converse of BPT,
=> DE II AB
Thus
=> angle CDE = angle A -------(2)
=> angle CED = Angle B -------(3)
From (1) , (2) and (3)
=> angle A = angle B
Thus
=> AC = BC (side opposite equal angles)
Thus ∆CAB is an isosceles triangle
Hence Proved
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