Question
From the diagram given below, which of the following option is true?
- ΔOBA and ΔOBC are congruent
- ΔOBA and ΔOBC are not congruent
- ∠ABO < ∠CBO
- ∠ABO > ∠CBO
Hint:
If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
The correct answer is: ΔOBA and ΔOBC are congruent
We can see in the diagram that AB = BC (given),
OB = OB (same side) and AO = OC (BO is bisector of the side AC).
Here, all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle.
Therefore, according to SSS rule, ΔOBA and ΔOBC are congruent
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