question_answer 7)

You have to show that \[\Delta AMP\cong \Delta AMQ\]. In the following proof, supply the missing reasons.

Steps	Reasons
(i) \[PM=QM\]
(ii) \[\angle PMA=\angle QMA\]
(iii) \[AM=AM\]
(iv) \[\Delta AMP\cong \Delta AMQ\]

Answer:

(i) \[PM=QM\]	(i) Given
(ii) \[\angle PMA=\angle QMA\]	(ii) Given
(iii) \[AM=AM\]	(iii) Common in both
(iv) \[\Delta AMP\cong \Delta AMQ\]	(iv) By SAS congruence criterion