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ABC and DBC are two triangles on the same base BC.and on the same side of BC with angle A=angleD=90 degrees. if CA and BD meet each other at E. Show that AE*EC=BE*ED

ABC and DBC are two triangles on the same base BC.and on the same side of BC with angle A=angleD=90 degrees. if CA and BD meet each other at E. Show that AE*EC=BE*ED

Grade:12

5 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
Please find the answer to your question below
Given : In triangles ABC and DBC
angle A=angleD=90 degrees
AC and BD intersect each other at E
To Prove : AE x EC = ED x BE
Proof : In triangles AEB and EDC,
and AEB = DEC..............(Vertically opposite angles)
triangle ABE ~ EDC
(EB/EC) = (AE/DE)
EB x DE = EC x AE
Hence, AE x EC = ED x BE
S. Haris Ahmed Irfan
29 Points
8 years ago
Please can you show the figure
SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
Please find the answer to your question below
Given : In triangles ABC and DBC
angle A=angleD=90 degrees
AC and BD intersect each other at E
To Prove : AE x EC = ED x BE
Proof : In triangles AEB and EDC,
and AEB = DEC..............(Vertically opposite angles)
triangle ABE ~ EDC
(EB/EC) = (AE/DE)
EB x DE = EC x AE
Hence, AE x EC = ED x BE240-2478_Untitled.png
gauri
23 Points
8 years ago
in triangle AEB n DEC
BY AA Triangles r similar
 THEN AE\ED=BE\CE
Then AE*CE=BE*ED
Kushagra Madhukar
askIITians Faculty 628 Points
2 years ago
Dear student,
Please find the attached solution to your peoblem.
240-2478_Untitled.png
Given : In triangles ABC and DBC
angle A=angleD=90 degrees
AC and BD intersect each other at E
To Prove : AE x EC = ED x BE
Proof : In triangles AEB and EDC, and AEB = DEC..............(Vertically opposite angles)
triangle ABE ~ EDC
(EB/EC) = (AE/DE)
EB x DE = EC x AE
Hence, AE x EC = ED x BE
 
Thanks and regards,
Kushagra

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