Question

information. if there needs to be more information, state none.
∠b≅∠y

1. ∠a≅∠z

bc≅yx

1. ∠c≅∠x

∠a≅∠z
ca≅xz

1. ac≅zx

∠b≅∠y
bc≅yx
zx≅ac

1. xy≅cb

∠x≅∠c
ab≅zy

1. ac≅zx

cb≅xy
m∠c = m∠x = 90

1. ab≅zy

cb≅xy

Explanation:

Step1: Recall triangle - congruence postulates

We have SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze each set of given information

For example, in 7, we have two angles and a non - included side equal, so it's AAS. In 8, two angles and the included side are equal, so it's ASA.

Step3: Determine congruence for each case

For 9: AAS. For 10: SAS. For 11: SSS. For 12: HL (since $\angle C=\angle X = 90^{\circ}$).

Answer:

1. AAS
2. ASA
3. AAS
4. SAS
5. SSS
6. HL