Question

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Explanation:

Step1: Analyze each triangle pair

1. $\triangle RNA \cong \triangle TAW$

• Identify right triangles: $\angle RNA = \angle TAW = 90^\circ$, $RA=TA$, $NA=WA$. Use HL (right triangles, hypotenuse+leg congruent).

2. $\triangle KTE \cong \triangle MET$

• $KT \parallel ME$ so $\angle K = \angle M$, $\angle KET = \angle MET$ (shared side $TE$), $KE=ME$. Use AAS.

3. $\triangle REN$

• Only two sides and non-included angle (SSA) → not enough information.

4. $\triangle VOB \cong \triangle FOD$

• $VO=FO$, $BO=DO$, $\angle VOB=\angle FOD$ (vertical angles). Use SAS.

5. $\triangle NAY \cong \triangle ZAH$

• Only one side and non-included angle → not enough information.

6. $\triangle HAT \cong \triangle HAC$

• $HT=HC$, $AH$ shared, $\angle T=\angle C=90^\circ$. Use HL (right triangles, hypotenuse+leg).

7. $\triangle KLB \cong \triangle RSB$

• $\angle L=\angle S=90^\circ$, $LB=SB$, $\angle KBL=\angle RBS$. Use ASA.

8. $\triangle MCA \cong \triangle FCA$

• $MC=FC$, $AC$ shared, $\angle MCA=\angle FCA$ (alternate interior angles, $MC\parallel FC$). Use SAS.

9. $\triangle RIP \cong \triangle HIP$

• $RI=HI$, $PI$ shared, $\angle RIP=\angle HIP=90^\circ$. Use HL (right triangles, hypotenuse+leg).

10. $\triangle PGU \cong \triangle WUT$

• $PU=WU$, $GU=TU$, $\angle P=\angle W$. Use ASA.

11. $\triangle BWJ \cong \triangle BEJ$

• $BW=BE$, $WJ=EJ$, $BJ$ shared. Use SSS.

12. $\triangle JAZ \cong \triangle RAZ$

• $\angle JZA=\angle RZA$, $AZ$ shared, $\angle JAZ=\angle RAZ$. Use ASA.

13. $\triangle CAP \cong \triangle TAP$

• $CA=TA$, $CP=TP$, $AP$ shared. Use SSS.

14. $\triangle DHS \cong \triangle FMS$

• $DH=FM$, $HS=MS$, $\angle DSH=\angle FSM$. Use SAS.

15. $\triangle ATP \cong \triangle LPH$

• $AT=LP$, $TP=PH$, $\angle ATP=\angle LPH=90^\circ$. Use SAS.

16. $\triangle VOK \cong \triangle JOG$

• $VO=JO$, $KO=GO$, $\angle VOK=\angle JOG$ (vertical angles). Use SAS.

Answer:

1. $\boldsymbol{\triangle RNA \cong \triangle TAW}$, HL
2. $\boldsymbol{\triangle KTE \cong \triangle MET}$, AAS
3. not enough information
4. $\boldsymbol{\triangle VOB \cong \triangle FOD}$, SAS
5. not enough information
6. $\boldsymbol{\triangle HAT \cong \triangle HAC}$, HL
7. $\boldsymbol{\triangle KLB \cong \triangle RSB}$, ASA
8. $\boldsymbol{\triangle MCA \cong \triangle FCA}$, SAS
9. $\boldsymbol{\triangle RIP \cong \triangle HIP}$, HL
10. $\boldsymbol{\triangle PGU \cong \triangle WUT}$, ASA
11. $\boldsymbol{\triangle BWJ \cong \triangle BEJ}$, SSS
12. $\boldsymbol{\triangle JAZ \cong \triangle RAZ}$, ASA
13. $\boldsymbol{\triangle CAP \cong \triangle TAP}$, SSS
14. $\boldsymbol{\triangle DHS \cong \triangle FMS}$, SAS
15. $\boldsymbol{\triangle ATP \cong \triangle LPH}$, SAS
16. $\boldsymbol{\triangle VOK \cong \triangle JOG}$, SAS