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Similar Triangles

Please write the fallowing notes on the board and go through the examples.

Similar polygo"s - Polygons that have the same shape, but different sizes; one polygon is an

enlargement or a reduction of the other polygon.

When two polygons are similar their corresponding (matching) angles are congruent (the same) AND the

lengths of the corresponding sides are in proportion, called the scale factor.

When two polygons are similar, we can write a similarity statement using the symbol "~,,

Scale factor - The ratio of corresponding lengths of two similar shapes

Example:

D.ABC and D.DEF are similar because their corresponding angles are equal and the ratio of their

corresponding sides are in proportion.

A L.A = Lt>0 tB:LE

LC:.Lt:\~ 4

AB BC ACc f F --=--=--B

3 r DE EF DFql \2 ~= 155O..I'Y\e o.~les -- - -D.ABC~ D.DEF ~ 3 5

Solving a triangle - Determining the measure of each angle in a triangle and the length of each side of

the triangle

*-**Remember the sum of angles in a triangle is 180·

Examples:

1. Find the missing angle and side in LlEFG (L E= ~ l 1=&= ~) (LE= ~3°,t 6-:::: +.qL{ CI'l1')

LE~ l~OO- Qoo-4-1°= ~3°OR be coose r-mh+ tn.nV\~(e:LE-:: q 00

- '-F/o =- 430--E

1~.OeMc"Z.::~c.. +b<-

~1o va.of·: (q.O)~ + b7..L...l--7f-.q-1f-C.....\-M~G- Jl Lf 4 - ~ \ = st;

f.Cf4 Cr>1.:: b GO2. If LlEFG is similar to LlHIJ in example 1, find the missing sides. (HI ::? l I J:: ?) (t\T.: 'l$.P" , )

OR. "Ie. ~ 1 C:J : ! :I:J - ~.~""em~~HJ I.j-"> Ratlre or rV~oyQS.E:l= "f.G-

C6.C eM HI ~ <60 IJ. ~:l:LLI' - -=- FG EG-lP.Oetfr q.O \~.O IJ _ <6.0

I J l-+I~{{{.o)(q·O) :t.q~-l~.O~ l'a .0 IJ::. (:J..qL()(~ .0) - s.a q CrY'

HI:: r;.0 LM 'a 0 -3. A building casts a shadow 72 metres long. At the same time, a parking meter that is 1.2 metres tall

casts a shadow that is 0.8 metres long. Determine the height of the building.* G~ s+Ud£nts to drCAW 'h"'to.r1gl-es. (04- leas{- ~)

DDD -ODDODDD -0 DODD

(\.a~~:: f@ (I.Q)L g o. sX :: (':1d)( t. a)

O.~'k.:: 10 cg yy\

1.2m~

12m O.8m

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