1. Teach GCSE Maths Congruent Triangles

2. Teach GCSE Maths Congruent Triangles © Christine Crisp "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

3. Congruent triangles form just one type of congruent shapes. However, they are very useful so it’s worth looking at them in more detail.

4. D E F A B C Congruent triangles have 3 pairs of equal sides. Sides AC and DF are a pair of equal sides The other pairs of equal sides are AB and DE, and BC and EF.

5. Which angle forms a pair with A? Which with B? And which with C? D E F A B C ANS: The pairs are A and D, B and E, C and F There are also 3 pairs of equal angles. Sides AC and DF are a pair of equal sides   Congruent triangles have 3 pairs of equal sides.

6. D E F A B C There are also 3 pairs of equal angles. Sides AC and DF are a pair of equal sides   We use a variety of symbols to mark angles. The same symbol in 2 or more angles means they are equal. Congruent triangles have 3 pairs of equal sides.

7. Equal sides are always opposite equal angles. e.g. If we are told that these triangles are congruent P Q S A C B   and QS = CA ( opposite the 90º angle ) BA ( opposite the angle with the cross ) So, PQ = CB ( 3 rd sides of the triangles ) PS =

8. X Y Z A B C 7 cm Equal sides are always opposite equal angles. XY = CA ( opposite ) X = C ( opposite the 7 cm sides)   So, XZ = BC ( 3 rd sides ) So, Y = A ( 3 rd angles )   e.g. If these are congruent  

9. SUMMARY  Equal sides are always opposite equal angles.  Congruent triangles have 3 pairs of equal sides and 3 pairs of equal angles. X Y Z A B C   Triangle XYZ and CAB are congruent.

10. Exercise 1. If these triangles are congruent, which sides are equal? Give the reasons. A B C X Y Z   2. If these triangles are congruent, which angles are equal? Give the reasons. A BC YZ X 6 cm 8 cm 6 cm 8 cm

11. Ans: AC = ZY ( opposite ) So, AB = ZX ( 3 rd sides ) BC = XY ( opposite  ) 1. If these triangles are congruent, which sides are equal? Give the reasons. A B C X Y Z   Exercise

12. 2. If these triangles are congruent, which angles are equal? Give the reasons. A BC YZ X C = X ( opposite the 6 cm sides )   6 cm 8 cm 6 cm 8 cm A = Z ( opposite the 8 cm sides )   B = Y ( 3 rd side of triangles )     Ans:

13. Suppose we put 2 right angled congruent triangles together like this: We now have an isosceles triangle. We can reverse this, so any isosceles triangle can be made into 2 right angled congruent triangles.

14. e.g. Since the triangles are congruent, these lengths... are equal. The line must be drawn from the vertex where the equal sides meet, vertex A. The perpendicular from A bisects the base. A We say that