~adapted from Walch Education Solving Problems Using Similarity and Congruence.
Unit 33 Congruence and Similarity
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Transcript of Unit 33 Congruence and Similarity
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Unit 33Congruence 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
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Unit 3333.1 Tests for Congruence
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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.?
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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.?
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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.?
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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.?
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Unit 3333.2 Congruent Triangles
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ABC and GHI ?
In each of the following, which triangles are congruent
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ABC and DEF and JKL?
In each of the following, which triangles are congruent
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ABC and DEF and JKL?
In each of the following, which triangles are congruent
?
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Unit 3333.3 Similar Shapes
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Which of these shapes are similar to shape A?
CDEGHI?
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Unit 3333.4 Similar Triangles
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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.
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Unit 3333.5 Line, Area and Volume
Ratios
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The diagram shows two similar cuboids
Volume of cuboid A = 60cm³Volume of cuboid B = 480cm³ Surface area of cuboid A = 94cm²Surface area of cuboid B = 374cm²
Lengths increase by a factor of 2Areas increase by a factor of 4 = 2²Volumes increase by a factor of 8 = 2³
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