Page 51 - Mathematics_Form_Two

Similarity

a Side-Side-Side (SSS) similarity
Example 3�5
theorem.
3. Two corresponding sides are For each pair of triangles in the
proportional and one pair of following figures, determine whether
corresponding angles (formed by these they are similar or not. Indicate the
FOR ONLINE READING ONLY
sides) are equal is described by the Side- similarity theorem used to support your
Angle-Side (SAS) similarity theorem. argument.

(a)
Angle-Angle (AA) similarity theorem Mathematics for Secondary Schools
The AA similarity theorem states that,
two triangles are similar if two pairs of
corresponding angles are equal. This
implies that, if two pairs of angles are
equal, the third pair of angles will also be
equal as described in Figure 3.3.

(b)

Figure 3�3: Similar triangles by the Angle-
Angle theorem

In Figure 3.3, it can be observed that,
ˆ
ˆ
ˆ
ˆ
BAC = QPR, ACB = PRQ (c)
ˆ
ˆ
Thus, ABC = PQR (third pairs of angles
of triangles)

Therefore, ABC ~ PQR  and

AB = BC = AC .
PQ QR PR Solution

(a) Required to prove that:
 OUL ~ MUO ,

45
Student's Book Form Two

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MATHEMATIC F2 v5.indd 45 11/10/2024 20:11:33
MATHEMATIC F2 v5.indd 45