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You want to show that $∆ART ≅ ∆PEN$,
$(a)$ If you have to use SSS criterion
$(a)$ Two triangles are said to be congruent by the SSS criterion if and only if, all the three sides of one triangle are equal to all the three sides of another triangle.
Hence, if $∆ ART ≅ ∆ PEN$ by SSS criterion, then
$(i).\ AR=PE$
$(ii).\ RT=EN$ and
$(iii).\ AT=PN$
$(b)$ Two triangles are said to be congruent by the SAS criterion if and only if two sides and the angle between them of one triangle are equal to the two sides and angle between them of another triangle.
Hence. if $∆ ART ≅ ∆ PEN$ by SAS criterion, and if it is given that $∠T=∠N$ by SAS criterion, then
$(i).\ RT=EN$
$(ii).\ PN=AT$
$(c)$. Two triangles are said to be congruent by the ASA criterion if and only if two angles and sides between them of one triangle are equal to the two angles and sides between them of another triangle.
Hence, if $∆ ART ≅ ∆ PEN$ by ASA criterion, and if it is given that $AT=PN$ by ASA criterion, then
$(i).\ ∠T=∠N$.
$(ii).\ ∠A=∠P$
Updated on: 10-Oct-2022
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