8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 1/10

 Wef W}jki`nf kig

jwq X}dxf}wjfq

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 2/10

 Wef W}jki`nf kig jwq X}dxf}wjfq

W}jki`nf jq k qjlxnf andqfg av}f lkgf do we}ff njif

qf`lfiwq)

W}jki`nf ekq we}ff f}wjafq. we}ff qjgfq kig we}ff ki`nfq)

 Ji Η KMA 

Qjgfq2 KM. MA kig AK

Ki`nfq2 ∨MKA. ∨KMA kig ∨MAK

_f}wjafq2 K. M kig A

Wef qjgf dxxdqjwf wd wef f}wfu K jq MA)

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 3/10

Mkqfg di wef qjgfq

Qaknfif W}jki`nfq

Id f{vkn qjgfq

Id f{vkn ki`nfq

Jqdqafnfq W}jki`nfqWpd f{vkn qjgfq

Wpd f{vkn ki`nfq

F{vjnkwf}kn W}jki`nfqWe}ff f{vkn qjgfq

We}ff f{vkn ki`nfq.

knpkzq ?8¸

Ankqqjojakwjdi do w}jki`nfq

Qaknfif 

Jqdqafnfq

F{vjnkwf}kn

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 4/10

 Ankqqjojakwjdi do w}jki`nfq

Mkqfg di Ki`nfq

Kavwf,ki`nfg W}jki`nf

Knn ki`nfq k}f nfqq weki :8¸ 

Dmwvqf,ki`nfg W}jki`nfEkq ki ki`nf ld}f weki :8¸ 

]j`ew,ki`nfg w}jki`nfq Ekq k }j`ew ki`nf %:8¸* 

Kavwf

W}jki`nf

]j`ew

W}jki`nf

Dmwvqf

W}jki`nf

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 5/10

 LFGJKIQ DO K W]JKI@NF  K lfgjki do k w}jki`nf jq k njif qf`lfiw bdjiji` 

k f}wfu wd wef ljgxdjiw do wef dxxdqjwf qjgf  K w}jki`nf ekq we}ff lfgjkiq)

• Wef we}ff lfgjkiq knpkzq lffw kw k qji`nf xdjiw)

• Fkae lfgjki gjjgfq wef w}jki`nf jiwd wpd qlknnf}

w}jki`nfq pejae ekf wef qklf k}fk 

•  Wef afiw}djg %xdjiw pef}f wefz lffw* jq wef afiwf} do `}kjwz do 

wef w}jki`nf

)

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 6/10

KNWJWVGFQ DO K W]JKI@NF • Knwjwvgf ‑ njif qf`lfiw o}dl k f}wfu

wekw jiwf}qfawq wef dxxdqjwf qjgf kw k}j`ew ki`nf)

Kiz w}jki`nf ekq we}ff knwjwvgfq)

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 7/10

Gfojijwjdi do ki Knwjwvgf do k W}jki`nf

 K qf`lfiw jq ki knwjwvgf do k w}jki`nf jo kig dinz jo jwekq dif figxdjiw kw k f}wfu do k w}jki`nf kig wefdwef} di wef njif wekw adiwkjiq wef qjgf dxxdqjwf wekwf}wfu qd wekw wef qf`lfiw jq xf}xfigjavnk} wd wejq njif)

 KAVWF DMWVQF

M

 K

A

KNWJWVGFQ DO K W]JKI@NF 

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 8/10

]J@EW

 K

M A

Jo  KMA jq k }j`ew w}jki`nf. jgfiwjoz jwq knwjwvgfq) 

M@. KM kig MA k}f jwq knwjwvgfq)

@

Aki k qjgf do k w}jki`nf mf jwq knwjwvgf4  ZFQ+

KNWJWVGFQ DO K W]JKI@NF 

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 9/10

X}ddo2  A # G # F < ;588    ))Qw}kj`ew njif 

K < G kig M < F )Knwf}ikwf ki`nfq

  A # M # K < ;588

K # M # A < ;588 

G  F

@jfi2 W}jki`nf

K M

A 

Adiqw}vawjdi2 G}kp njif ―n‚ we}dv`e A xk}knnfn

wd wef mkqf KM

Wef lfkqv}f do wef we}ff ki`nfq do k w}jki`nf qvl 

wd ;58 8 

) Wd X}df 2  K # M # A < ;588

n

KI@NF QVL X]DXF]WZ DO K W]JKI@NF 

8/2/2019 The E Tutor - Properties of Triangle

http://slidepdf.com/reader/full/the-e-tutor-properties-of-triangle 10/10

Ki fuwf}jd} ki`nf do k w}jki`nf f{vknq wef qvl do wef wpd jiwf}jd} dxxdqjwf ki`nfq ji lfkqv}f)

Wd X}df2  KAG < KMA # MKA 

X}ddo2  AM # KAG < ;588        ) Qw}kj`ew njif

KMA # KAM # MKA < ;588        qvl do wef w}jki`nf 

KAM # KAG < KMA # KAM # MKA

KAG < KMA # MKA

K

M A G

@jfi2 Ji Η KMA fuwfig MA

wd G

FUWF]JD] KI@NF DO K W]JKI@NF KIG

JWQ X]DXF]WZ