1 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use Similar Triangles Stage 6 - Year 11 General Mathematics Preliminary

2 Similar Figures (1/7) Similar If two objects are identical apart from size then they are Similar. Reduction Reduction (Smaller) Enlargement Enlargement (Larger) proportion Similar figures are in proportion 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 equal. A B C X Y Z  A =  X  B =  Y  C =  Z  ∆ABC ||| ∆XYZ Means Similar

5 Similarity Test 1 (4/7) Corresponding angle are equal. M L N S R T  L =  R  M =  S  N =  T  ∆LMN ||| ∆RST Only two are needed for a triangle. 90 o 50 o 40 o

6 Similarity Tests 2 (5/7) Pairs of Corresponding Sides are in the same Ratio 4cm 6cm 5cm 2cm 3cm 2.5 cm 63  ∆ABC ||| ∆XYZ = 52.5 = 42 = 2= 2 A B C Y X Z

7 Scale Factors (6/7) Scale Factor is the ratio of First:Second with the First reduced to 1 4cm 3cm 7cm 14cm 6cm 8cm First : Second 6 : 3 ÷6 ÷6 1 : 12 Scale Factor = 12 1st 2nd Scale Factor=1 Congruent. If Scale Factor=1 then the shapes are Congruent. Scale Factors Web

8 Scale Factors (7/7) Scale Factor is the ratio of First:Second with the First reduced to 1 6cm 3cm 9cm 3cm 1cm 2cm First : Second 3 : 9 ÷3 ÷3 1 : 3 Scale Factor = 3 1st 2nd Scale Factor=1 Congruent. If Scale Factor=1 then the shapes are Congruent. Puzzle Web