91Ó°ÊÓ

$SSS$- Side – Side – Side method means if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

$SAS$– Side – Angle – side method means if two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, then triangles are congruent.

$ASA$- Angle – side – angle method means if two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, then triangles are congruent.

$AAS$– Angle – angle – side method if two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, then triangles are congruent.

$HL$– Hypotenuse – leg method means if the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, then two triangles are congruent.

It is given that $\stackrel{¯}{AO}âŠ\yen \text{±è±ô²¹²Ô±ð }M$and also $\stackrel{¯}{BO}â‰\dots \stackrel{¯}{CO}$.

In order to prove the congruency of triangles $\mathrm{Δ}\text{AOB}$and $\mathrm{Δ}\text{AOC}$of which sides, $BO$and $OC$lies on plane $M$observe the following:

i. It is given that,$\text{BO}â‰\dots \text{CO}$.

ii. Since, $\stackrel{→}{\text{AO}}âŠ\yen$plane M, so, $\text{AO}âŠ\yen \text{BO}$and $\text{AO}âŠ\yen \text{OC}$, which implies that $∠\text{AOB}â‰\dots ∠\text{AOC}$.

iii. Side $\text{AO}=\text{OA}$is common in both triangles.

Therefore, by $SAS$congruency $\mathrm{Δ}\text{AOB}â‰\dots \mathrm{Δ}\text{AOC}$.