In Fig- P L - O A and P M - O B such that P L-P M- Is P L O - P M O - Give reasons in support of your answer-

Given: nbsp; nbsp; nbsp;PL⊥ OAPM⊥ OBPL=PMIn Δ PLO nbsp; and Δ PMO,∠ PLO=∠ PMO=90^∘ (∵ PL⊥ OA and PM ⊥ OB )Hypotenuse PO= Hypotenuse PO (Common side)PL= ...

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Standard VII

Mathematics

Triangle

In Fig. P L ⊥...

Question

In Figure, $P L ⊥ O A$ and $P M ⊥ O B$ such that $P L = P M$ . Is $Δ P L O ≅ Δ P M O$ ?
Give reasons in support of your answer.

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Solution

Given:
$P L ⊥ O A$
$P M ⊥ O B$
$P L = P M$
In $Δ P L O$ and $Δ P M O$ ,
$∠ P L O = ∠ P M O = 90^{\circ}$ ( $∵ P L ⊥ O A$ and $P M ⊥ O B$ )
$Hypotenuse P O = Hypotenuse P O$ (Common side)
$P L = P M$ (Given)
By RHS congruence property, $Δ P L O ≅ Δ P M O$
Therefore, $Δ P L O ≅ Δ P M O$ is true by RHS congruence property.

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In Figure, PL⊥OA and PM⊥OB such that PL=PM. Is ΔPLO≅ΔPMO?Give reasons in support of your answer.

Given: PL⊥OAPM⊥OBPL=PMIn ΔPLO and ΔPMO,∠PLO=∠PMO=90∘ (∵PL⊥OA and PM⊥OB )Hypotenuse PO=Hypotenuse PO (Common side)PL=PM (Given)By RHS congruence property, ΔPLO≅ΔPMOTherefore, ΔPLO≅ΔPMO is true by RHS congruence property.

In Figure, $P L ⊥ O A$ and $P M ⊥ O B$ such that $P L = P M$ . Is $Δ P L O ≅ Δ P M O$ ?
Give reasons in support of your answer.