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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

S. Haris Ahmed Irfan , 10 Years ago
Grade 12
anser 5 Answers
SHAIK AASIF AHAMED

Last Activity: 10 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

Last Activity: 10 Years ago

Please can you show the figure

SHAIK AASIF AHAMED

Last Activity: 10 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

Last Activity: 10 Years ago

in triangle AEB n DEC
BY AA Triangles r similar
 THEN AE\ED=BE\CE
Then AE*CE=BE*ED

Kushagra Madhukar

Last Activity: 4 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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