Page 96 - Start Up Mathematics_6

5. Measure the sides of the adjacent triangle and verify: C

(a) AB + BC > CA
(b) BC + CA > AB
(c) CA + AB > BC
A B

Magnitude of an Angle B
∠AOB is the magnitude of the rotation about the vertex O
through which the initial ray OA goes through to reach the
terminal position OB.

Comparison of Angles O A

Following are the two methods by which the given angles are compared:
(i) By observation (ii) By tracing

Comparison by observation: At times it is convenient to compare the given angles by mere
observation:
A
P

O Q
B R
Clearly, ∠AOB > ∠PQR.

Comparison by tracing: Let’s compare two angles ∠AOB and ∠PQR.
(a) Keep a tracing paper on ∠AOB and trace it.

(b) Now put this traced copy of ∠AOB on ∠PQR such that O coincides with Q and OB falls
along QR.

(c) There could be three possibilities:
 If OA falls between QR and QP, then ∠AOB < ∠PQR.

 If OA coincides with QP, then ∠AOB = ∠PQR.

 If OA falls beyond QP, then ∠AOB > ∠PQR.

P(A) (A)
P
(A) P

Q(O) R(B) Q(O) R(B) Q(O) R(B)

∠AOB < ∠PQR ∠AOB = ∠PQR ∠AOB > ∠PQR

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