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Comparing Angles by Superimposition

Angles can be compared by the method of superimpositon.

Consider ∠AOB and ∠CDE.

B E

A
O
D C
To compare the two angles, we trace ∠AOB on a tracing paper and proceed as follows:

Step 1: Combine the vertices of these angles by Step 2: Align side OA with side DC.
superimposing point O to point D.

E E
B
B
A A
D(O) C D(O) C

E
Step 3: Now combine the angles such that sides OB and DE fall on the B
same side as OA and DC are superimposed over each other.
A
D(O) C
Step 4: Since side OB lies inside angle CDE, hence ∠AOB < ∠CDE.

Conclusion: Any two angles can be compared with the method of superimposition. It is worth to
note that while superimposing, the vertices of the angles must overlap. Superimpositon tells us
whether the angles being compared are larger, smaller or equal to each other.

Quick Check
1. In the given figure, determine which angle is greater and why:
(a) ∠AOY or ∠XOY A X
(b) ∠AOC or ∠XOY
(c) ∠YOB or ∠YOC
Y
2. Can you say which angle is greater: ∠XOY or ∠AOB?
O
B C
A
X
Y

O B

To overcome from the situation given in question 2 (above), we need to know the magnitude of
the angles.

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