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

2. 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. 3 House Plan (2/7) Plans are an example of a scale drawing.

4. 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. 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. 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. 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. 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