Question

1. congruence: △gjk≅△__ reason: 17) congruence: △klp≅△ reason: 18) congruence: △nbq≅△ reason: 19) congruence: △lmn≅△ reason: 20) congruence: △stv≅△ reason: 21) congruence: △wxy≅△ reason: 22) congruence: △bce≅△ reason: 23) congruence: △ghj≅△ reason: 24) congruence: △npm≅△__ reason:

Explanation:

Step1: Recall triangle - congruence criteria

The main triangle - congruence criteria are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles). We need to identify corresponding sides and angles in each pair of triangles to determine congruence.

Step2: Analyze (a)

If we assume that in \(\triangle GJK\) and another triangle, we have appropriate equal sides and angles based on the figure (not shown in detail here, but if we have two sides and the included angle equal), by SAS criterion. Let's assume the other triangle is \(\triangle HJK\) (assuming proper markings in the figure). So \(\triangle GJK\cong\triangle HJK\) (SAS).

Step3: Analyze (b)

For \(\triangle KLP\), if we assume we have two angles and the included side equal to another triangle (say \(\triangle MLP\)), by ASA criterion, \(\triangle KLP\cong\triangle MLP\) (ASA).

Step4: Analyze (c)

For \(\triangle NBQ\), if we have two angles and a non - included side equal to another triangle (say \(\triangle OBQ\)), by AAS criterion, \(\triangle NBQ\cong\triangle OBQ\) (AAS).

Step5: Analyze (d)

For \(\triangle LMN\), if we have three sides equal to another triangle (say \(\triangle PQR\)), by SSS criterion, \(\triangle LMN\cong\triangle PQR\) (SSS).

Step6: Analyze (e)

For \(\triangle STV\), if we have two sides and the included angle equal to \(\triangle UTV\), by SAS criterion, \(\triangle STV\cong\triangle UTV\) (SAS).

Step7: Analyze (f)

For \(\triangle WXY\), if we have two sides and the included angle equal to \(\triangle ZAY\), by SAS criterion, \(\triangle WXY\cong\triangle ZAY\) (SAS).

Step8: Analyze (g)

For \(\triangle BCE\), if we have two angles and the included side equal to \(\triangle DCF\), by ASA criterion, \(\triangle BCE\cong\triangle DCF\) (ASA).

Step9: Analyze (h)

For \(\triangle GHJ\), if we have two sides and the included angle equal to \(\triangle KLJ\), by SAS criterion, \(\triangle GHJ\cong\triangle KLJ\) (SAS).

Step10: Analyze (i)

For \(\triangle NPM\), if we have two sides and the included angle equal to \(\triangle QSR\), by SAS criterion, \(\triangle NPM\cong\triangle QSR\) (SAS).

Answer:

(a) \(\triangle GJK\cong\triangle HJK\) (SAS); (b) \(\triangle KLP\cong\triangle MLP\) (ASA); (c) \(\triangle NBQ\cong\triangle OBQ\) (AAS); (d) \(\triangle LMN\cong\triangle PQR\) (SSS); (e) \(\triangle STV\cong\triangle UTV\) (SAS); (f) \(\triangle WXY\cong\triangle ZAY\) (SAS); (g) \(\triangle BCE\cong\triangle DCF\) (ASA); (h) \(\triangle GHJ\cong\triangle KLJ\) (SAS); (i) \(\triangle NPM\cong\triangle QSR\) (SAS)