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Exploring Congruence and Similarity in Triangles: Tests, Examples, and Applications

This unit covers tests for congruence including SSS, SAS, AAS, and RHS, as well as exploring congruent and similar triangles and shapes. Learn to identify congruent triangles and similar shapes using various methods and solve related problems involving lengths, angles, and ratios. Dive into line, area, and volume ratios, and understand the relationships between similar geometric figures. Enhance your understanding of congruence and similarity through practical examples and exercises in this comprehensive unit.

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Exploring Congruence and Similarity in Triangles: Tests, Examples, and Applications

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  1. Unit 33Congruence and Similarity

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

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

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

  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. Triangles ABC, PQR and HIJ are all similar. 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° ? ? ? ?

  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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