Question

(a)not necessarily congruentcongruent:△uvw≅△□by theselect(b)not necessarily congruentcongruent:△abc≅△□by theselect(c)not necessarily congruentcongruent:△mno≅△□by theselect

Explanation:

(a)

Step1: Identify corresponding angles and sides

In \(\triangle UVW\) and \(\triangle ZXY\), we have two angles (\(\angle V=\angle Y\), \(\angle W = \angle X\)) and a non - included side (the side marked with one tick) equal.

Step2: Apply congruence criterion

By the \(AAS\) (Angle - Angle - Side) congruence criterion, \(\triangle UVW\cong\triangle ZXY\)

(b)

Step1: Identify corresponding angles and sides

In \(\triangle ABC\) and \(\triangle DEF\), we have two angles (\(\angle B=\angle D\), \(\angle C=\angle E\)) and a non - included side (the side marked with one tick) equal.

Step2: Apply congruence criterion

By the \(AAS\) (Angle - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle DEF\)

(c)

Step1: Analyze given information

We have two sides equal (marked with one and two ticks respectively) but no information about angles.

Step2: Determine congruence

Since we do not have enough information (either \(SSS\), \(SAS\), \(ASA\), \(AAS\) or \(HL\) for right - angled triangles) to prove congruence, \(\triangle MNO\) and \(\triangle QRP\) are not necessarily congruent.

Answer:

(a) Congruent: \(\triangle UVW\cong\triangle ZXY\) by the \(AAS\) (Angle - Angle - Side)
(b) Congruent: \(\triangle ABC\cong\triangle DEF\) by the \(AAS\) (Angle - Angle - Side)
(c) Not Necessarily Congruent