Mathematics 10 Page 1 of 5 Properties of Triangle s and Quadrilaterals. Isosceles Triangle. - 2 sides and 2 corresponding.

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1 Mthemtis 10 Pge 1 of 5 Properties of s Pthgoren Theorem used to find the length of sides of right tringle Tpe of s nd Some s Theorems ngles s Slene Isoseles Equilterl ute - ll ngles re less thn 90 o -ll 3 sides nd ngles re different nd re less thn 90 o - 2 sides nd 2 orresponding ngles re sme - ll sides nd ngles re sme. Right - ll 3 sides nd ngles re - one ngle is 90 o different nd 1 ngle is 90 o - 2 sides nd 2 orresponding ngles re sme, the 3 rd ngle is 90 o Otuse - one ngle is greter thn 90 o -ll 3 sides nd ngles re different nd one ngle is greter thn 90 o - 2 sides nd 2 orresponding ngles re sme, the 3 rd ngle is greter thn 90 o si ngle Theorems/uthorities omplementr ngles () Opposite ngle Theorem (OT) If, then + = 90 or, + = 90 Supplementr ngles (S) If is stright line, then _ + _ = _180_ or + = _180_ Sum of ngles in Theorem (STT) E If nd re line segments interseting t E, then, = nd, = In n tringle, the sum of the ngles is 180 o Tht is: + + = 180 o

2 Mthemtis 10 Pge 2 of 5 Eerise: Find the unknon ngles indited nd sho ork (inluding uthorities in the rkets) ) ) ) d) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) e) f) g) h) 70 = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) i) j) k) l) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) m) n) o) p) = ( ) = ( ) = ( ) = ( ) nsers: ll ngles re in degrees ) 30 ) 120, 60, 120 ) 105, 150 d) 50, 80 e) 80, 80, 30 f) 150, 30 g) 45 h) 60, 60 i) 80, 100, 80 j) 40, 140, 40 k) 150, 80, 110 l) 60, 120 m) 35 n) 80 o) 65 p) 30

3 Mthemtis 10 Pge 3 of 5 Prllel Line Theorem (PLT) lternte ngle Theorem (Z) lines, then the lternte ngles re equl. orresponding ngle Theorem (F) lines, then the orresponding ngles re equl. Interior ngle Theorem () lines, then the interior ngles re supplementr. d Trnsversl + = 180 o + d = 180 o Eerise Stte the vlues of the unknons (inluding uthorities in the rkets) ) ) ) d) 38 o 55 o 120 o 130 o = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) e) f) g) 40 o h) d 55 o 100 o 30 o 70 o 35 o 56 o = ( ) = ( ) = ( ) d = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) nsers: ll ngles re in degrees ) 38, 142 ) 125, 55 ) 120, 60 d) 130, 50, 130 e) 80, 80, 25, 55 f) 30, 80, 80 g) 40, 40, 320 h) 56, 56, 89

4 Mthemtis 10 Pge 4 of 5 Properties of s Medins: Midpoint: ltitude: Perpendiulr isetors: ngle isetors: entroid: Orthoentre: irumentre: Inentre: line from verte to the midpoint of the opposite side point on line tht divides it into 2 equl prts to dr medin find mid point of opposite side nd onnet to verte shos the height of polgon to dr n ltitude line from verte to opposite side so tht it meets t 90 perpendiulr to line segment nd meets t its midpoint. to dr perpendiulr isetor find midpoint, then mesure right ngle, dr line. The (interior) isetor of n ngle, lso lled the internl ngle isetor is the line or line segment tht divides the ngle into to equl prts here ll 3 medins meet divides eh medin in the rtio 1: 2 it is the entre of mss here ll 3 ltitudes meet here ll 3 perpendiulr isetors meet entre of the irle tht psses through the verties of the tringle the irle is lled irumirle or irumsried irle here ll 3 ngle isetors meet entre of the irle tht meets eh side one the irle is lled inirle or insried irle medin entroid ltitude orthoentre perpendiulr isetor irumentre ngle isetor Inentre v v

5 Mthemtis 10 Pge 5 of 5 Properties of Qudrilterl Wht is qudrilterl? Polgon ith 4 sides nd sum of the ngles is 360 o Qudrilterl Piture esription & Properties n Qudrilterl Polgon ith 4 sides Sum of ngles is 360 o Squre Qudrilterl ith 4 sides re equl ll ngles re 90 o igonls re perpendiulr to eh other Retngle Rhomus Prllelogrm Qudrilterl ith 2 pirs of equl opposite sides ll ngles re 90 o igonls re not perpendiulr to eh other Qudrilterl ith 4 sides re equl None of ngles is 90 o pir of ute ngles nd pir of otuse ngles igonls re perpendiulr to eh other Qudrilterl ith 2 pirs of equl opposite sides None of ngles is 90 o pir of ute ngles nd pir of otuse ngles igonls re not perpendiulr to eh other Kite Qudrilterl ith 2 pirs of equl djent sides igonls re perpendiulr to eh other Trpeoid Qudrilterl ith 1 pir of unequl ut prllel opposite sides

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