Question

(c) If it is given that AT = PN and you are to use ASA criterion, you need to have

(i) ? (ii) ?​

Answer 1

According to ASA 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 AT=PN in the given two triangles.

The triangles are congruent if,

∠RAT=∠EPN

∠ATR=∠PNE

Answer 2

If it is given that AT = PN and you are to use ASA criterion, you need to have (i) ∠A = ∠P (ii) ∠T = ∠N

It is given that we need to use the ASA criterion, in this, we need to equate two angles and a side that lies between the two angles.

Therefore to apply this criterion we need to have the angles equal. We know that AT = PN, therefore the angels on the ends of this side are ∠A, ∠T on the ends of AT, and ∠P, ∠N at the ends of side PN.

Therefore we need to have  (i) ∠A = ∠P (ii) ∠T = ∠N