If △ABC≅△PQR, which of the following need NOT be NECESSARILY true?

Correct option is A

Given:

△ABC≅△PQR,

Solution:

Analysis each option given that △ABC≅△PQR,

Option (a) $$m(\overline{AB}) = m(\overline{PQ}); \, m(\overline{BC}) = m(\overline{RP}); \, \angle A = \angle P$$​​

​​This option suggests that segment $$\overline BC$$​ in △ABC  corresponds to segment $$\overline{RP}$$​ in △PQR This is incorrect because, in congruent triangles, $$\overline{BC}$$​ should correspond to $$\overline{QR}$$​. Therefore, this option need not be necessarily true.

Option (b) $$m(\overline{AB}) = m(\overline{PQ}); \, m(\overline{BC}) = m(\overline{QR}); \, m(\overline{CA}) = m(\overline{PR})$$​​

​​This option states that all corresponding sides in both triangles are equal in length. This is a true condition for congruent triangles, so this option must be true.

Option (c) $$m(\overline{AB}) = m(\overline{PQ}); \, m(\overline{BC}) = m(\overline{QR}); \, \angle A = \angle P$$​​

​​This option states that two corresponding sides and one corresponding angle are equal. While these conditions are necessary, they are not sufficient on their own to guarantee triangle congruence. Therefore, this option need not be necessarily true.

Option (d) $$∠A=∠P;∠B=∠Q;∠C=∠R$$​​

​​This option states that all corresponding angles in both triangles are equal. This is a necessary condition for congruent triangles, so this option must be true.

Thus, correct option is (a)