This document covers the topics of congruence, similarity, and ratios between similar shapes. It includes 4 tests for determining if triangles are congruent based on side lengths and angles. It also discusses identifying similar shapes and using corresponding parts of similar triangles to determine unknown lengths and angles. Finally, it examines how linear dimensions, areas, and volumes are scaled between similar cuboids based on common scale factors.

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