Question

1. congruence: △kjm≡△__ reason: 8) congruence: △npr≡△ reason: 9) congruence: △stu≡△ reason: 10) congruence: △xyz≡△ reason: 11) congruence: △deg≡△ reason: 12) congruence: △hjk≡△ reason: 13) congruence: △stv≡△ reason: 14) congruence: △wxy≡△ reason: 15) congruence: △bcf≡△__ reason:

Explanation:

Step1: Identify congruent triangles by side - side - side (SSS) or side - angle - side (SAS) etc.

For 7: In $\triangle KJM$ and $\triangle LMK$, we can see that the corresponding sides are equal. Since $KJ = LM$, $JM=MK$, and $KM = LK$ (common side), by SSS (Side - Side - Side) congruence criterion.

Step2: Write the congruent triangle

$\triangle KJM\cong\triangle LMK$

Step3: For 8: In $\triangle NPR$ and $\triangle QPR$, $NP = QP$, $PR=PR$ (common side), $NR = QR$. By SSS, $\triangle NPR\cong\triangle QPR$

Step4: For 9: In $\triangle STU$ and $\triangle VWU$, $ST = VW$, $\angle STU=\angle VWU$ (vertically - opposite angles), $TU = WU$. By SAS (Side - Angle - Side), $\triangle STU\cong\triangle VWU$

Step5: For 10: In $\triangle XYZ$ and $\triangle BAY$, $XY = BA$, $\angle XYZ=\angle BAY$ (vertically - opposite angles), $YZ = AY$. By SAS, $\triangle XYZ\cong\triangle BAY$

Step6: For 11: In $\triangle DEG$ and $\triangle FEG$, $DE = FE$, $EG = EG$ (common side), $DG = FG$. By SSS, $\triangle DEG\cong\triangle FEG$

Step7: For 12: In $\triangle HJK$ and $\triangle MLK$, $HJ = ML$, $\angle HJK=\angle MLK$ (vertically - opposite angles), $JK = LK$. By SAS, $\triangle HJK\cong\triangle MLK$

Step8: For 13: In $\triangle STV$ and $\triangle UTV$, $ST = UV$, $TV = TV$ (common side), $SV = TU$. By SSS, $\triangle STV\cong\triangle UTV$

Step9: For 14: In $\triangle WXY$ and $\triangle ZAY$, $WX = ZA$, $\angle WXY=\angle ZAY = 90^{\circ}$, $XY = AY$. By SAS, $\triangle WXY\cong\triangle ZAY$

Step10: For 15: In $\triangle BCF$ and $\triangle DCE$, $BC = DC$, $\angle BCF=\angle DCE$ (vertically - opposite angles), $CF = CE$. By SAS, $\triangle BCF\cong\triangle DCE$

Answer:

1. $\triangle KJM\cong\triangle LMK$, Reason: SSS
2. $\triangle NPR\cong\triangle QPR$, Reason: SSS
3. $\triangle STU\cong\triangle VWU$, Reason: SAS
4. $\triangle XYZ\cong\triangle BAY$, Reason: SAS
5. $\triangle DEG\cong\triangle FEG$, Reason: SSS
6. $\triangle HJK\cong\triangle MLK$, Reason: SAS
7. $\triangle STV\cong\triangle UTV$, Reason: SSS
8. $\triangle WXY\cong\triangle ZAY$, Reason: SAS
9. $\triangle BCF\cong\triangle DCE$, Reason: SAS