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10 grade maths> ABC and DBC are two triangles on the same...

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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 AEEC=BEED

S. Haris Ahmed Irfan , 11 Years ago

Grade 12

5 Answers

SHAIK AASIF AHAMED

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

Last Activity: 11 Years ago

S. Haris Ahmed Irfan

Please can you show the figure

Last Activity: 11 Years ago

SHAIK AASIF AHAMED

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

Last Activity: 11 Years ago

gauri

in triangle AEB n DEC

BY AA Triangles r similar

THEN AE\ED=BE\CE

Then AE*CE=BE*ED

Last Activity: 11 Years ago

Kushagra Madhukar

Dear student,

Please find the attached solution to your peoblem.

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

Last Activity: 5 Years ago

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