a c = A C AD DB = BD

Transcription

1 1.) SIMILR TRINGLES.) Some possile proportions: Geometry Review- M.. Sntilli = = = = =.) For right tringle ut y its ltitude = = =.) Or for ll possiilities, split into 3 similr tringles: ll orresponding sides re proportionl.

2 .) PRLLEL LINES UT Y TRNSVERSL 180Þ- 180Þ- 180Þ- 180Þ- 3.) NGLE OF REFLETION For perpendiulr mirrors, the inident ry will e prllel to the refleted ry: ll 4.) TRINGLES.) + + = 180 o nd = +.) ongruent Tringles: S SSS

3 S SS HL PT- orresponding Prts of ongruent Tringles re ongruent.) Similr Tringles (orresponding sides re therefore proportionl): SSS (similr sides) SS (similr sides)

4 d.) ISOSELES THEOREM: se ngles re ongruent. e.) LTITUES of tringle interset t the ORTHOENTER: Orthoenter f.) MEINS of tringle interset t the ENTROI: y (,) entroid (lning Point) entroid ( (+)/3, /3) (0,0) (,0) x g.) NGLE ISETORS of tringle interset t the INENTER: Inenter (enter of the lrgest insried irle)

5 h.) PERPENIULR ISETORS of tringle interset t the IRUMENTER: irumenter (enter of the smllest irumsried irle) i.) ny point on the ngle isetor is equidistnt to the two sides of the ngle, i.e., =. j.) re of tringle: =1/h h = k.) re of tringle y the use of only the sides (Heron s Theorem) s(s )(s )(s ) where s = 1 ( + + ) = semiperimeter

6 l.) Pythgoren Theorem: + = (for right tringles) m.) sinα Lw of the sines: = sinβ = sinγ Lw of the osines: = + osγ β γ α 5.) POLYGONS (n-gons):.) Sum of regulr polygon s interior ngle = 180(n )o where n= numer of sides. 180(n ) o Mesurement of eh interior ngle =.) Sum of regulr polygon s exterior ngles = 360 o. 360 o Mesurement of eh exterior ngle = n n.) re of polygon: = p where p= perimeter nd = pothem

7 d.) 4-gons (qudrilterl): 1.) Squre: i.) Perimeter: P = 4 ii.) re: =.) Retngle: i.) Perimeter: P = + ii.) re: = 3.) Rhomus i.) Perimeter P = 4 ii.) re: = h h 4.) prllelogrm i.) Perimeter: P = + = h ii.) re: h

8 5.) trpezoid i.) Perimeter: P = ii.) re: = h( + ) = hm where m is the midsegment iii.) djent ngles re supplementry ( i.e., m α + m β = 180 o ) 6.) rrowhed i.) Perimeter: P = + ii.) re: = h α β h m h e.) Str Polygons: ( verties efore onnetion. n m gons ) where n= totl numer of verties nd m= numer of 1.) Mesurement of str polygon s vertex ngle =.) Mesurement of str polygon s exterior (turn) ngle = 180 n m n m 360 o m n o = entrl ngle

9 3.) exmple: 5/gon 4 1 V E 3 5 5/ gon = 5 verties, onneting every other (see numering ove) Mesurement of str polygon s vertex ngle V= = 36 o 5 Mesurement of str polygon s exterior (turn) ngle E= entrl ngle = 360o () 5 o = 144 o 6.) IRLES:.) r length of setor: s θ = π or s θ = πr π or s = rθ.) re of setor: θ = πr π or = 1 r θ θ s r

10 .) m α = m nd m = 1 m, where m is the mesurement of the r α d.) m α = 1 m + α e.) m α = 1 m α α f.) Power of the point Q: P Q = ( Q) ( Q) = ( Q) ( Q) Q g.) Power of the point Q: P Q = ( Q) ( Q)= ( Q) ( Q) Q

11 h.) Power of the point Q: P Q = ( Q) = ( Q) ( Q) Q f.) = or =, where +=dimeter 7.) SIMILR SOLIS:.) Surfe res etween similr solids: S 1 = Edge 1 S Edge.) Volumes etween similr solids: V 1 = Edge 1 V Edge 3