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Similar TrianglesSimilar TrianglesStage 6 - Year 11Stage 6 - Year 11

General MathematicsPreliminary

2

Similar Figures (1/7)

If two objects are identical apart from size then they are SimilarSimilar.

ReductionReduction (Smaller)

EnlargementEnlargement (Larger)

Similar figures are in proportionproportion and have the same shape.

3

House Plan (2/7)

Plans are an example of a scale drawing.

4

Similarity Test 1 (3/7)

Corresponding angles are equalCorresponding angles are equal..

AA

BB

CC

XX

YY

ZZ

A = A = XX

B = B = YY

C = C = ZZ

∆ ∆ABC ||| ∆XYZ ABC ||| ∆XYZ

Means SimilarMeans Similar

5

Similarity Test 1 (4/7)

Corresponding angle are equalCorresponding angle are equal..

MM

LL

NN

SS

RR

TT

L = L = RR

M = M = SS

N = N = TT

∆ ∆LMNLMN ||| ∆ ||| ∆RSTRST

Only two are Only two are needed for a needed for a

triangle.triangle.

9090oo9090oo

5050oo

5050oo

4040oo

4040oo

6

Similarity Tests 2 (5/7)

Pairs of Corresponding Sides are Pairs of Corresponding Sides are in the same Ratioin the same Ratio

4cm4cm6cm6cm

5cm5cm

2c2cmm

3cm3cm

2.5 cm2.5 cm

6633 ∆ ∆ABCABC ||| ∆ ||| ∆XYZXYZ = 55

2.52.5= 44

22= 2

AA

BB

CC

YY

XX

ZZ

7

Scale Factors (6/7)

Scale Factor is the ratio of Scale Factor is the ratio of First:Second First:Second with thewith the First First reduced reduced

toto 1 1

4c4cmm3cm3cm

7cm7cm14cm14cm

6cm6cm

8cm8cm

First : First : SecondSecond 6 : 3 6 : 3

÷6 ÷6 ÷6 ÷6

1 : 1 : 1122

Scale Factor = Scale Factor = 1122

1st1st 2nd2nd

If Scale Scale Factor=1Factor=1 then the shapes are CongruentCongruent..

Scale FactorsScale FactorsWeb Web

8

Scale Factors (7/7)

Scale Factor is the ratio of Scale Factor is the ratio of First:Second First:Second with thewith the First First reduced reduced

toto 1 1

6c6cmm3cm3cm

9cm9cm3cm3cm

1cm1cm

2cm2cm

First : First : SecondSecond 3 : 9 3 : 9

÷3 ÷3 ÷3 ÷3

1 : 1 : 33

Scale Factor = Scale Factor = 33

1st1st

2nd2nd

If Scale Scale Factor=1Factor=1 then the shapes are CongruentCongruent..

PuzzlePuzzleWeb Web