Question

for each pair of triangles, determine what additional information is needed to prove the triangles congruent using the reason provided. then, write the trinngle congruence statement.

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

Explanation:

Step1: Recall congruence criteria

SAS: Side - Angle - Side, two sides and included angle. SSS: Side - Side - Side, all three sides. ASA: Angle - Side - Angle, two angles and included side. HL: Hypotenuse - Leg for right - triangles.

Step2: Analyze each pair

For 19, with two sides given, need included - angle. For 20, with two sides given, need third side. For 21, with two angles and one side, need the other included - angle. For 22, with one side and included - angle, need the other side. For 23, for right - triangles, need hypotenuse. For 24, with two sides given, need third side. Then write congruence statements.

Answer:

1. Need $\angle LKM=\angle GIH$, $\triangle LKM\cong\triangle GIH$.
2. Need $DX = ZY$, $\triangle DXZ\cong\triangle ZYX$.
3. Need $\angle WUV=\angle KVM$, $\triangle WUV\cong\triangle KVM$.
4. Need $DE = DC$, $\triangle DEC\cong\triangle DTC$.
5. Need $HK = HL$, $\triangle HMK\cong\triangle HML$.
6. Need $RT = YX$, $\triangle RTS\cong\triangle YXZ$.