You want to show that $Δ A R T ≅ Δ P E N$ .
If it is given that $A T = P N$ and you are to use ASA criterion, you need to have
i) ?
ii) ?

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Solution

According to $A S A$ criterion , If two angles and their included side in one triangle are equal to the two angles and their included side in other triangle, then the triangles are congruent.

So, if side $A T = P N$ in the given two triangles.
The triangles are congruent if,

$∠ R A T = ∠ E P N$
$∠ A T R = ∠ P N E$

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Similar questions

You want to show that ΔART ≅ ΔPEN,

(a) If you have to use SSS criterion, then you need to show

(i) AR = (ii) RT = (iii) AT =

(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have

(i) RT = and (ii) PN =

(i) ? (ii) ?

Question 2 (c)
You want to show that $Δ A R T ≅ Δ P E N$ :
If it is given that AT = PN and you are to use ASA criterion, you need to have:
i) ? (ii)?

Δ A R T ≅ Δ P E N

A S A, S A S, S S S

Δ A R T ≅ Δ P E N

∠ T = ∠ N

Δ A R T ≅ Δ P E N

∠ T = ∠ N

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