Question

In the given figure,\[PL \bot OA\]and \[PM \bot OB\]such that PL=PM. Is\[\Delta PLO \cong PMO\]?. 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: \[PL \bot OA\] and\[PM \bot OB\];
\[ \Rightarrow \angle PLO = {90^0}\] and \[\angle PMO = {90^0}\]
Now, In \[\Delta PLO\] and \[\Delta PMO\];
PO=PO (common in both triangles)
PL=PM (given in question)
\[\angle PLO\]=\[\angle PMO = {90^0}\]
Using RHS congruence rule,
\[\Delta PLO \cong \Delta PMO\].

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.