Download UNIT 33 Congruence and Similarity Teaching Notes

MEP Jamaica: STRAND I
UNIT 33 Congruence and Similarity: Teaching Notes
UNIT 33 Congruence and Similarity
Teaching Notes
Introduction
This is an important and vital unit in the Strand I, Geometry and Trigonometry needed for the work in
other units.
Teaching Points
Two concepts are covered in this unit, congruence and similarity. Shapes which are congruent are
identical whereas those that are similar have angles that are of equal size and corresponding sides in
the same ratio. So shapes that are congruent are also similar, but similar shapes are not necessarily
congruent.
Language / Notation
• congruent
• similar
• scale factor
Key points
• Congruent shapes are identical but can have different orientations.
For example, these five shapes are all congruent.
• Similar shapes have corresponding angles equal and corresponding sides in the same ratio.
For example, shapes A, B, C, D and E are all similar; B and D are also congruent.
B
C
D
E
A
• We have used triangles to illustrate congruence and similarity but it should be stressed that these
concepts can be used with any 2-dimensional shapes.
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MEP Jamaica: STRAND I
UNIT 33 Congruence and Similarity: Teaching Notes
UNIT 33 Congruence and Similarity
Teaching Notes
Misconceptions
• Confusion between congruence and similarity
• Not realising that
and
are congruent (that is, orientation does not matter)
• Not realising that similar shapes have sides in the same ratio, so the two triangles shown in
diagram A are similar (perpendicular sides both in ratio 2 : 1)
Diagram A
but the two triangles in Diagram B are not similar (perpendicular sides in the ratio 9 : 4 and 7 : 3).
Diagram B
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