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Standard X

Mathematics

AAA Similarity

ii CD and GH ...

Question

Question 10 (ii)
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
$(i i) Δ D C B \sim Δ H G E$

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Solution

(ii) In $Δ D C B a n d Δ H G E$ ,
$∠ D C B = ∠ H G E$ (Halves of $∠$ BCA and $∠$ FGE)
$∠ B = ∠ E$ (Because it is given that $Δ A B C \sim Δ F E G$ )
$∴ Δ D C B \sim Δ H G E$ (By AAA similarity criterion)

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Similar questions

Q. Question 10 (ii)
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) Δ D C B \sim Δ H G E

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 (ii) 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 (ii)ΔDCB∼ΔHGE

(ii) In ΔDCB and ΔHGE, ∠DCB=∠HGE (Halves of ∠BCA and ∠FGE) ∠B=∠E (Because it is given that ΔABC∼ΔFEG) ∴ΔDCB∼ΔHGE (By AAA similarity criterion)

Question 10 (ii)
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
$(i i) Δ D C B \sim Δ H G E$

(ii) In $Δ D C B a n d Δ H G E$ ,
$∠ D C B = ∠ H G E$ (Halves of $∠$ BCA and $∠$ FGE)
$∠ B = ∠ E$ (Because it is given that $Δ A B C \sim Δ F E G$ )
$∴ Δ D C B \sim Δ H G E$ (By AAA similarity criterion)