Page 57 - Mathematics_Form_Two

Similarity

Side-Side-Side (SSS) similarity theorem
The SSS similarity theorem states that, two triangles are similar if three pairs of
corresponding sides are proportional. Figure 3.4 describes the SSS theorem.

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Mathematics for Secondary Schools

Figure 3�4: Similar triangles by the Side-Side-Side theorem

In Figure 3.4, it can be observed that, if the ratio of their sides are such that

LM = LN = MN , then ∆LMN ∼ ∆DEF

DE DF EF
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
Therefore, LMN = DEF, MNL = EFD and MLN = EDF.
Example 3�9
With reasons, identify a pair of triangles which are similar in each of the following
triangles.

Solution YZ 6 3
To show that the triangles are similar, Ratio of remaining sides: PQ = 10 = 5
find the ratio of the lengths of
corresponding sides (shortest, longest The ratios of the corresponding sides
and the remaining sides). are not all equal. Therefore XYZ∆ and
∆ PQR are not similar.
Comparing XYZ∆ and PQR∆
XY 4 1 Comparing XYZ∆ and EFG∆
Ratio of shortest sides: = =
PR 8 2 Considering ∆XYZ and ∆PQR:

XZ 8 1 XY 4 2
Ratio of longest sides: = = Ratio of shortest sides: = =
QR 16 2 EF 10 5

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Student's Book Form Two

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