Question

state what additional information is required to know that the triangles are congruent for the reason given.

1. sss
2. sas
3. asa
4. aas
5. hl
6. sas

Explanation:

Step1: Recall congruence criteria

For SSS, all 3 - side pairs must be equal. For SAS, 2 - side and included - angle pairs. For ASA, 2 - angle and included - side pairs. For AAS, 2 - angle and non - included side pairs. For HL, hypotenuse and one leg in right - triangles.

Step2: Analyze each case

1. Need $JK = GK$. 14. Need $\angle{UWV}=\angle{DCB}$. 15. Need $\angle{XZY}=\angle{JIX}$. 16. Need $\angle{RQP}=\angle{LQN}$. 17. Need $CI = JI$. 18. Need $\angle{KJI}=\angle{STI}$.

Answer:

1. $JK = GK$
2. $\angle{UWV}=\angle{DCB}$
3. $\angle{XZY}=\angle{JIX}$
4. $\angle{RQP}=\angle{LQN}$
5. $CI = JI$
6. $\angle{KJI}=\angle{STI}$