Question

In the given figure,$$PL\mathrm{\perp }OA$$and $$PM\mathrm{\perp }OB$$such that PL=PM. Is$$\mathrm{\Delta }PLO\cong PMO$$?. Give reason in support of your answer.

Answer 1

Hint:
RHS congruence rule: If in two right angled triangles, hypotenuse and one side of the triangle is equal to the hypotenuse and one side of another triangle, then the two triangles are congruent.

Complete step by step solution:
Given: $$PL\mathrm{\perp }OA$$ and$$PM\mathrm{\perp }OB$$;
$$\Rightarrow \mathrm{\angle }PLO={90}^0$$ and $$\mathrm{\angle }PMO={90}^0$$
Now, In $$\mathrm{\Delta }PLO$$ and $$\mathrm{\Delta }PMO$$;
PO=PO (common in both triangles)
PL=PM (given in question)
$$\mathrm{\angle }PLO$$=$$\mathrm{\angle }PMO={90}^0$$
Using RHS congruence rule,
$$\mathrm{\Delta }PLO\cong \mathrm{\Delta }PMO$$.

Note:
$$\cong$$implies congruence of triangles. When two triangles are congruent then they will have exactly the same three sides and exactly the same three angles. RHS congruence stands for Right angle-Hypotenuse – side congruence.