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In the figure given below, OL is perpendicular to AB and OM is perpendicular to BC such that $OL = OM$ . Is $△ OLB ≅ ΔOMB ?$

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True

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answer is A.

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Detailed Solution

Here, we have,

OL = OM

Here, OL is perpendicular to AB and OM is perpendicular to BC. Thus,

∠ OLB = ∠ OMB = 90^{o}

In right angle triangle OLB by the Pythagoras theorem,

{OL}^{2} + {BL}^{2} = {OB}^{2}

{OM}^{2} + {BM}^{2} = {OB}^{2}

{OL}^{2} + {BL}^{2} = {OM}^{2} + {BM}^{2}

{BL}^{2} = {BM}^{2}

BL = BM

Since,

∠ OLB = ∠ OMB

OL = OM

Thus, by side-angle side congruence criteria of congruency,

ΔOLB ≅ △ OMB

Correct option is1.

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