Page 46 - Mathematics_Form_Two

Similarity

Example 3�2
ˆ
Given that ABC ~ PQR,  find the value of ABC if:
(a) BAC 120 and PRQ = ˆ ° ˆ = 25°

(b) QPR BCA + ˆ ˆ = 145°

Mathematics for Secondary Schools Consider the following figures of ABC and PQR. 25º R
Solution

C

120º
A B
ˆ
ˆ
ˆ
ˆ
(a) Since QRP corresponds to BCA , then QRP = BCA = 25°.
ˆ
ˆ
ˆ
(sum of interior angles in a triangle)
+
+
=
In ABC, ABC BCA BAC  FOR ONLINE READING ONLY
180
ˆ
ABC 25 120 + °+ ° = 180°
ˆ
145° =
°−
35 .°
Thus, ABC 182= = 1800 − 1450 = 350.
ˆ
Therefore, ABC 35 .= °
ˆ
ˆ
ˆ
ˆ
(b) Since QPR corresponds to BAC, then QPR = BAC.
ˆ ˆ ˆ
Thus, QPR BCA+ QPR BCA+ ˆ ˆ ˆ ˆ = = CAB BCA 120+ BAC BCA 120+ CAB ˆ ˆ = ° = + + 25° ° = 25° 145° 145° = .
But ABC BAC ACB + ˆ ˆ + ˆ = 180° (sum of interior angles in a triangle). It
follows that
145 ABC °+ ˆ = 180°
ˆ
ABC = 180°-145°=35°.
180° – 145° = 35°
ˆ
Therefore, ABC 35 .= °
Example 3�3
In the following figure, name the triangles which are similar and determine the
constant of proportionality needed to show their similarity.

40
Student's Book Form Two

11/10/2024 20:11:29
MATHEMATIC F2 v5.indd 40
MATHEMATIC F2 v5.indd 40 11/10/2024 20:11:29