Question

(a) not necessarily congruent congruent: △uvw ≅ △ by the select (b) not necessarily congruent congruent: △mno ≅ △ by the select (c) not necessarily congruent congruent: △abc ≅ △ by the select

Explanation:

(a)

Step1: Identify corresponding parts

In \(\triangle UVW\) and \(\triangle YXZ\), we have \(UV = YX\) (marked with one tick), \(\angle V=\angle X\) (given), \(VW = XZ\) (marked with one tick).

Step2: Apply congruence criterion

By the Side - Angle - Side (SAS) congruence criterion, \(\triangle UVW\cong\triangle YXZ\).

(b)

Step1: Analyze given information

In \(\triangle MNO\), we have three sides marked with ticks. In \(\triangle PQR\), we have two sides marked with ticks and one angle. There is not enough information to establish congruence. For example, the Side - Side - Angle (SSA) is not a valid congruence criterion.

(c)

Step1: Identify vertical angles

\(\angle ABC=\angle DBE\) (vertical angles are equal). Also, \(AB = DE\) (marked with one tick), \(BC=BD\) (marked with one tick).

Step2: Apply congruence criterion

By the Side - Angle - Side (SAS) congruence criterion, \(\triangle ABC\cong\triangle EDB\).

Answer:

(a) Congruent: \(\triangle UVW\cong\triangle YXZ\) by the SAS (Side - Angle - Side) criterion.
(b) Not Necessarily Congruent.
(c) Congruent: \(\triangle ABC\cong\triangle EDB\) by the SAS (Side - Angle - Side) criterion.