Math, asked by shamithD, 9 months ago

prove that if two triangles are equiangler then their corresponding sides are proportional​

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Answers

Answered by Ashu21sufu03
8

Hi,

here u go with ur answer..

According to Greek mathematician Thales, “The ratio of any two corresponding sides in two equiangular triangles is always the same.” ... If in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

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Answered by manitisawant
4

Answer:

Prove that

"If two triangles are equiangular then their corresponding sides are proportional

ANSWER

Data : In △ABC and △DEF

∠BAC=∠EDF

∠ABC=∠DEF

To prove :

DE

AB

=

EF

BC

=

FD

CA

Construction : Mark points G and H on AB and AC such that AG=DE and AH=DF. Join G and H.

Proof : In △AGH and △DEF

AG=DE∵Construction

∠GAH=∠EDF∵Data

AH=DF∴Construction

∴△AGH≅△DEF∵SAS

∠AGH=∠DEF

But, ∠ABC=∠DEF

⇒∠AGH=∠ABC

∴GH∥BC.

In △ABC=

AG

AB

=

GH

BC

=

HA

CA

Hence

DE

AB

=

EF

BC

hope it helps

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