1. Unit 33 Congruence and Similarity Presentation 1Tests for Congruence Presentation 2Congruent Triangles Presentation 3Similar Shapes Presentation 4Similar Triangles Presentation 5Line, Area and Volume Ratios

2. Unit 33 33.1 Tests for Congruence

3. Test 1 (side, side side) If all three sides of one triangle are the same as the lengths of the sides of the second triangle, then the two triangles are congruent This is referred to as SSS. ?

4. Test 2 (side, angle, side) If two sides of one triangle are the same length as two sides of the other and the angle between these two sides is the same in both triangles, then the triangles are congruent. This is referred to as SAS. ?

5. Test 3 (angle, angle, side) If two angles and the length of one side are the same in both triangles then they are congruent. This is referred to as AAS. ?

6. Test 4 (right angle, hypotenuse, side) If both triangles contain a right angle, have hypotenuses of the same length and one other side of the same length, then they are congruent. This is referred to as RHS. ?

7. Unit 33 33.2 Congruent Triangles

8. ABC and GHI ? In each of the following, which triangles are congruent

9. ABC and DEF and JKL ? In each of the following, which triangles are congruent ?

10. ABC and DEF and JKL ? In each of the following, which triangles are congruent ?

11. Unit 33 33.3 Similar Shapes

12. Which of these shapes are similar to shape A? C D E G H I ? ? ? ? ? ?

13. Unit 33 33.4 Similar Triangles

14. What is: (a) the length of CB. 5cm (b) the length of IJ.12.5cm (c) the size of angle PQR.65° (d) the size of angle ABC.65° ? Triangles ABC, PQR and HIJ are all similar. ? ? ?

15. Unit 33 33.5 Line, Area and Volume Ratios

16. The diagram shows two similar cuboids Volume of cuboid A = 60cm³ Volume of cuboid B = 480cm³ Surface area of cuboid A = 94cm² Surface area of cuboid B = 374cm² Lengths increase by a factor of 2 Areas increase by a factor of 4 = 2² Volumes increase by a factor of 8 = 2³ ? ? ? ? ? ? ?