1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Congruent Triangles Stage 6 - Year 11 Mathematic ( Preliminary )

2 Two triangles are congruent if they are both the same size and shape. For Example 6cm 8cm 70 o 7cm 75 o 35 o Congruent Triangles 1

3 Two triangles are congruent if. All the three Sides of the triangles are equal in length. SSS 6cm 8cm 7cm Congruent Triangles 2

4 Two triangles are congruent if. Two pairs of corresponding Sides and the included Angle are equal. SAS 6cm 8cm 70 o Congruent Triangles 3

5 Two triangles are congruent if. Two pairs of Angles and any pair of corresponding Sides are equal. AAS 8cm 70 o 75 o Congruent Triangles 4

6 Two triangles are congruent if. Both have a Right angle. The Hypotenuses and one pair of corresponding Sides are equal. RHS 8cm 7cm 8cm 7cm Congruent Triangles 5

7 Example 1 A B C 10cm 3.4cm 9.4cm P Q R 10cm 3.4cm 9.4cm AB = PQ (Corresponding Sides) BC = QR (Corresponding Sides) AC = PR (Corresponding Sides) Therefore Congruent by SSS Congruent Triangles 6

8 Example 2 A B C 3.4cm 9.4cm P Q R 3.4cm 9.4cm AB = PQ (Corresponding Sides) BC = QR (Corresponding Sides)  B =  Q (Included angle) Therefore Congruent by SAS Congruent Triangles 7

9 Example 3 A B C 10cm 70 o 20 o P Q R 10cm 70 o 20 o  A =  P (Corresponding Angles)  C =  R (Corresponding Angles) AC = PR (Corresponding Sides) Therefore Congruent by AAS Congruent Triangles 8

10 Example 4 A B C 10cm 3.4cm P Q R 10cm 3.4cm  B =  Q = 90 o (Right Angle) AC = PR (Hypotenuse) BC = QR (Corresponding Sides) Therefore Congruent by RHS Congruent Triangles 9