Page 60 - Mathematics_Form_Two

Similarity

Example 3�10 Ratio of the shortest sides:

Given the following triangles, prove that AE 3cm 3 1
∆ ABC and XYZ∆ are similar. AD = (3 6 cm = 9 = 3
)
+

Ratio of the longest sides: = 7 = 1
FOR ONLINE READING ONLY
7cm
Mathematics for Secondary Schools Proof AB 3 1 AC AE = + CAD (Common).
AB
=
)
(7 14 cm
3
21
=
BAE ∠
∠
AB
1
Thus
=
and
3
AD
AC
Ratio of shortest sides:
CAD
∠
BAE ∠
.
XY
BC = 15 = 1 5 Therefore, ACD∆ = ∼∆ ABE.
4
Ratio of longest sides: = =
YZ 20 5
ˆ
ˆ (given)
ABC = XYZ Activity 3�3: Exploring similarity
through perpendicular
AB BC 1 bisectors
ˆ
ˆ
Thus, = = and ABC = XYZ
XY YZ 5 1. Use a geometrical software of your
choice (or any other method) to
Therefore, ABC∆  ∆ XYZ. (SAS draw a triangle PQR∆ .
theorem)
2. Construct a line perpendicular to
QR through point P , and label the
Example 3�11 intersection as S.
Given the following figure, show that 3. Measure segments PQ , PS , PR ,
∆ AED ∼∆ ABE . and RS.
4. Calculate the ratios PQ and PR .
PC PS
PQ PR
5. Drag point C until = .
PS RS
6. For which value of ∠ PQR are
∆ PQR and PRS∆ similar?
7. Share your findings about the
theorem that supports your answer
in task 6, and explain how it applies
Solution to the similarity observed in this
From ACD∆ and ABE∆ activity.

54
Student's Book Form Two

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MATHEMATIC F2 v5.indd 54