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Standard X

Mathematics

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iii CD and GH...

Question

Question 10 (iii)
CD and GH are respectively the bisectors of $a n g l e A C B$ and $∠ E G F$ such that D and H lie on sides AB and FE of $Δ A B C$ and $Δ E F G$ respectively. If $Δ A B C \sim Δ F E G$ , Show that
$(i i i) Δ D C A \sim Δ H G F$

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Solution

(iii) In $Δ D C A a n d Δ H G F$ ,
$∠ A C D = ∠ F G H$ (CD and GH are bisectors of $∠ A C B$ and $∠ E G F$ ,also it is given that $Δ A B C \sim Δ F E G$ )
$∠ A = ∠ F$ ( $Δ A B C \sim Δ F E G$ )
$∴ Δ D C A \sim Δ H G F$ (By AAA similarity criterion)

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Similar questions

Q. Question 10 (iii)
CD and GH are respectively the bisectors of

a n g l e A C B

and

∠ E G F

such that D and H lie on sides AB and FE of

Δ A B C

and

Δ E F G

respectively. If

Δ A B C \sim Δ F E G

, Show that

(i i i) Δ D C A \sim Δ H G F

CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ∼ ΔFEG, Show that:

(i)

(ii) ΔDCB ∼ ΔHGE

(iii) ΔDCA ∼ ΔHGF

Q. Question 10 (i)
CD and GH are respectively the bisectors of

∠ A C B a n d ∠ E G F

such that D and H lie on sides AB and FE of

Δ A B C

and

Δ E F G

respectively. If

Δ A B C \sim Δ F E G

, Show that

(i) \frac{C D}{G H} = \frac{A C}{F G}

Q. Question 10 (i)
CD and GH are respectively the bisectors of

∠ A C B a n d ∠ E G F

such that D and H lie on sides AB and FE of

Δ A B C

and

Δ E F G

respectively. If

Δ A B C \sim Δ F E G

, Show that

(i) \frac{C D}{G H} = \frac{A C}{F G}

C D

and

G H

are respectively the bisectors of

∠ A C B

and

∠ E G F

such that

D

and

H

lie on the sides

A B

and

F E

△ A B C

and

△ E F G

. If

△ A B C \sim △ E F G

, show that,

\frac{C D}{G H} = \frac{A C}{F G}

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AAA Similarity

Standard X Mathematics

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Question 10 (iii) CD and GH are respectively the bisectors of angleACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC∼ΔFEG, Show that (iii)ΔDCA∼ΔHGF

(iii) In ΔDCAandΔHGF, ∠ACD=∠FGH (CD and GH are bisectors of ∠ACB and ∠EGF ,also it is given thatΔABC∼ΔFEG) ∠A=∠F ( ΔABC∼ΔFEG) ∴ΔDCA∼ΔHGF (By AAA similarity criterion)

Question 10 (iii)
CD and GH are respectively the bisectors of $a n g l e A C B$ and $∠ E G F$ such that D and H lie on sides AB and FE of $Δ A B C$ and $Δ E F G$ respectively. If $Δ A B C \sim Δ F E G$ , Show that
$(i i i) Δ D C A \sim Δ H G F$

(iii) In $Δ D C A a n d Δ H G F$ ,
$∠ A C D = ∠ F G H$ (CD and GH are bisectors of $∠ A C B$ and $∠ E G F$ ,also it is given that $Δ A B C \sim Δ F E G$ )
$∠ A = ∠ F$ ( $Δ A B C \sim Δ F E G$ )
$∴ Δ D C A \sim Δ H G F$ (By AAA similarity criterion)