Page 45 - Mathematics_Form_Two

Similarity

C
R
70º 4 cm 70º

5 cm 3.75 cm 3 cm

FOR ONLINE READING ONLY
50º 60º 50º 60º
P Q
A 6 cm B 4.5 cm
Figure 3�2: Similar triangles
ˆ
ˆ
From Figure 3.2, CAB of ABC corresponds to RPQ of PQR and each measures Mathematics for Secondary Schools
ˆ
ˆ
ˆ
50°, ABC corresponds to PQR and each measures 60°, and BCA corresponds to
ˆ
QRP and each measures 70°.
Since the corresponding angles are equal, then the two triangles are similar. Also, AB
corresponds to PQ, BC corresponds to QR, and CA corresponds to RP. The ratios of
the corresponding sides are given by:

4
4
AB = 6 cm =, BC = 4 cm = 4 and CA = 5 cm =.
PQ 4.5 cm 3 QR 3 cm 3 RP 3.75 cm 3
AB BC CA 4
Therefore, = = =.
PQ QR RP 3

Since the corresponding sides are proportional, the two triangles are similar. Therefore,
ΔABC is similar to ΔPQR and is denoted by ΔABC ~ ΔPQR. The symbol ~ means
“similar to.”

Similar triangles (polygons) are named according to the order of their vertices.
For instance, in ΔABC and ΔPQR in Figure 3.2, it can be deduced from the order
of the vertices that AB of the first triangle corresponds to PQ of the second triangle.

Consequently, BC corresponds to QR, and AC corresponds to PR.

Example 3�1
ˆ
ˆ
ˆ
to NFR, KSL corresponds to RNF,
Given that ∆SLK∼∆NFR, identify ˆ ˆ
all the corresponding angles and the and LKS corresponds to FRN. Also,
corresponding sides. LS of SLK corresponds to FN of

Solution ∆NFR, SK of ∆SLK corresponds to
Using the order of vertices of the two NR of NFR,D and KL of SLKD

ˆ
similar triangles, SLK corresponds corresponds to RF of  NFR.

39
Student's Book Form Two

11/10/2024 20:11:28
MATHEMATIC F2 v5.indd 39 11/10/2024 20:11:28
MATHEMATIC F2 v5.indd 39