1. What’s the same, what’s different?
Starter
What’s the same, what’s different?

2. Which coloured shape is mathematically similar to this white one?

3. Which coloured shape is mathematically similar to this white one?

4. Which coloured shape is mathematically similar to this white one?

5. Which coloured shape is mathematically similar to this white one?

6. Are these triangles similar?  = yes,  = no,  = not sure
6 cm
10 cm
5 cm
3 cm
4 cm
8 cm

7. Are these squares similar?  = yes,  = no,  = not sure
6 cm
2 cm
2 cm
6 cm

8. Are these rectangles similar?  = yes,  = no,  = not sure
6 cm
2 cm
10 cm
4 cm

9. Are these rectangles similar?  = yes,  = no,  = not sure
4 cm
5 cm
2 cm
10 cm

10. Are these shapes similar?  = yes,  = no,  = not sure
X cm
7 cm
3 cm
15 cm

11. What about if I tell you they ARE mathematically similar.
X cm
7 cm
Could you calculate x?
3 cm
15 cm

12. X cm
7 cm
These two represent the same side
3 cm
15 cm

13. X cm 7 cm 3 cm 15 cm Write as a ratio 3 : 15 Simplify 1 : 5
This number is the scale factor
15 cm

14. x 5
35 cm
X cm
7 cm
3 cm
15 cm

15. These two shapes are mathematically similar.
Calculate x.
Write as a ratio
8 : 12
Simplify
1 : 1.5
12 cm
8 cm
10 cm
15 cm
x cm
x 1.5

16. These two shapes are mathematically similar.
Calculate x.
Write as a ratio
10 : 25
Simplify
1 : 2.5
25 cm
10 cm
18 cm
x cm
45 cm
÷ 2.5

17. Answers 1) x = 7.5 cm 2) x = 6.25 cm 3) x = 8.33 cm 4) x = 4.5 cm
y = 7 cm
5) x = 11.2 cm
y = 12.5 cm
6) x = 6.45 cm
7) x = 4 cm
y = 1.5 cm
8) x = 4.5 cm
y = 9 cm
9) x = 1.6 cm
10) x = 4.8 cm
y = 5.33 cm

18. Starter Calculate a, b, c and d. sf 2 But 9 x 2 isn’t 36?!!!!!!!!!!
9 cm²
36 cm²
4 cm
2 cm
b cm²
d cm²
c cm
4.5 cm
a cm
9 cm
But 9 x 2 isn’t 36?!!!!!!!!!!

19. Linear SF = 3
Area SF = 3² = 9
Volume SF = 3³ = 27
4cm
Why?
12cm

20. 160
Area = _____cm²
Area = 40cm² 2
Linear SF = ___ 4
Area SF = ___
6cm
12cm

21. 648
Volume = ______cm³
Volume = 24cm³ 9
Area SF = ___ 3
Linear SF = ___ 27
Volume SF = ___
Surface area = 32cm²
Surface area = 288cm²

22. Answers 1) Linear SF = 2 Area SF = 4 Volume SF = 8 2) Linear SF = 1.5
5a) 6 cm
5b) 3.375
6) 80 cm
7a) £17.62
7b) 3.92 or 4 people
8) 3.9 kg

23. What’s the same? What’s different?
Starter
What’s the same? What’s different?
4cm
42°
6cm
6cm
42°
9cm
4cm
6cm
42°
32°
8cm
4cm

24. Definitions
Congruent shapes have all sides and angles equal.
Similar shapes have all angles equal but one is an enlargement of the other.

25. Are these triangles congruent?
Congruence
Are these triangles congruent?
For triangles to be congruent, three properties must be the same:
SSS
6cm
6cm
4cm
3.5cm
4cm
3.5cm

26. Are these triangles congruent?
Congruence
Are these triangles congruent?
For triangles to be congruent, three properties must be the same:
SAS
4cm
3.5cm
78°
78°
4cm
3.5cm

27. Are these triangles congruent?
Congruence
Are these triangles congruent?
For triangles to be congruent, three properties must be the same:
ASA
47°
4cm
78°
47°
78°
4cm

28. Are these triangles congruent?
Congruence
Are these triangles congruent?
For triangles to be congruent, three properties must be the same:
RHS
5cm
5cm
4cm
Right angle, hypotenuse, side
4cm

29. Are these triangles congruent?

30. Are these triangles congruent?

31. Are these triangles congruent?

32. Are these triangles congruent?

33. Are these triangles congruent?

34. Are these triangles congruent?

35. Are these triangles congruent?

36. Are these triangles congruent?

37. Are these triangles congruent?

38. PR = PQ (isosceles triangle) Angles RPQ = QPR (same angle)
Diagram NOT accurately drawn
Triangle PQR is isosceles with PQ = PR. X is a point on PQ. Y is a point on PR. PX = PY.
Prove that triangle PQY is congruent to triangle PRX
(Total 3 marks)
PX = PY (as in question)
PR = PQ (isosceles triangle)
Angles RPQ = QPR (same angle)
SAS proves triangles are congruent.

39. Create your own question on proving congruence or similarity.
Plenary
Create your own question on proving congruence or similarity.
Make sure you have provided enough information on your diagram.