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8/14/2019 Thaless Theorem

1/7

GOVT SR. SEC SCHOOL,HAIBOWAL KHURDGOVT SR. SEC SCHOOL,HAIBOWAL KHURDLUDHIANALUDHIANA

1010 thth classclassBy: Navneet KadBy: Navneet Kad

THALES THEOREMTHALES THEOREM
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THALES THEOREMTHALES THEOREMOROR

BASICBASICPROPORTIONALITYPROPORTIONALITY

THEOREMTHEOREM
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STATEMENTSTATEMENT

If in a triangle a line is drawnIf in a triangle a line is drawnparallel to its one side, then itparallel to its one side, then it

will divide the other twowill divide the other twosides in same proportionsides in same proportion
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GIVENGIVEN

AA triangletriangle A BCA BCinin whichwhich aa lineline

parallelparallel toto BCBC isisdrawndrawn whichwhichintersectsintersects A BA B atatpointpoint DD andand A CA Catat pointpoint EE..

A

B C

D E
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TO PRO VE:TO PRO VE:

A D A EA D A E

BD EC

A

B C

D E
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C O NS TRU C T IO NC O NS TRU C T IO N

J oin BE A nd CD.J oin BE A nd CD.

Draw EF A B.Draw EF A B.

Draw DG A C.Draw DG A C.

A

B C

D EF G
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PROOF :PROOF :ar ( A DE)ar ( A DE)

ar (BDE)ar (BDE)

A

B

C

D EF

1/2 X A D X EF

1/2 X BD X EFA DBD

ar ( A DE)ar ( A DE)ar (BDE)ar (BDE)ar ( A DE)ar ( A DE)ar (CDE)ar (CDE)

1/2

1/2

X A E XDGX EC X DG

G

A E

ECar (BDE)= ar(CDE) Because both triangles lie on samebase DE and two parallel lines DE

and BC.

(1)

(2)

Putting in equation (2)

ar ( A DE) A Ear ( A DE) A Ear (BDE) ECar (BDE) EC

(3)

From equation (2) & (3)A D A EDB EC

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