state what additional information is required in order to know that the triangles are congruent for the reason given.
6) asa
7) aas
8) sas
9) sss
10) aas

Question

Accepted Answer

### Problem 6: ASA
# Explanation:
## Step1: Recall ASA Criterion
ASA (Angle - Side - Angle) congruence requires two angles and the included side to be equal. In the diagram with triangles $ \triangle KIE $ and $ \triangle FDE $ (assuming the intersection at $ E $), we know $ \angle I=\angle D $ (right angles or marked angles) and $ \angle KEI=\angle FED $ (vertical angles).
## Step2: Identify Missing Part
To apply ASA, we need the included side between the two angles. So we need $ EI = DE $ (or the sides forming the vertical angles with the equal angles) to have the included side equal.

# Answer: We need $ EI = DE $ (or the included side between the two known equal angles to be equal)

### Problem 7: AAS
# Explanation:
## Step1: Recall AAS Criterion
AAS (Angle - Angle - Side) congruence requires two angles and a non - included side to be equal. In the diagram with triangles $ \triangle ABC $ and $ \triangle FBE $ (intersecting at $ B $), we know $ \angle A=\angle F $ (maybe from the diagram) and $ \angle ABC=\angle FBE $ (vertical angles).
## Step2: Identify Missing Part
We need a non - included side. For example, if we consider angles at $ A, B $ in $ \triangle ABC $ and at $ F, B $ in $ \triangle FBE $, we need $ AC = FE $ (a non - included side) to apply AAS.

# Answer: We need $ AC = FE $ (a non - included side equal)

### Problem 8: SAS
# Explanation:
## Step1: Recall SAS Criterion
SAS (Side - Angle - Side) congruence requires two sides and the included angle to be equal. In triangles $ \triangle VWU $ and $ \triangle KML $, we know one side is marked equal (e.g., $ VU = ML $) and we need the included angle and another side. The included angle is $ \angle V $ and $ \angle K $, so we need $ \angle V=\angle K $ and $ VW = KM $ (or $ VU = ML $ is already marked, so we need the included angle $ \angle V=\angle K $ and another side like $ VW = KM $) to apply SAS.
## Step2: Identify Missing Part
We need $ \angle V=\angle K $ (the included angle) and $ VW = KM $ (the other side) to satisfy SAS.

# Answer: We need $ \angle V=\angle K $ and $ VW = KM $ (or the included angle and the other side equal)

### Problem 9: SSS
# Explanation:
## Step1: Recall SSS Criterion
SSS (Side - Side - Side) congruence requires all three sides to be equal. In the rhombus - like figure with triangles $ \triangle STR $ and $ \triangle SMR $, we know $ ST = SR $ (marked) and $ TR = MR $ (common side).
## Step2: Identify Missing Part
We need $ SM = ST $ (or $ SM = SR $) to have all three sides equal. So we need $ SM = ST $ to apply SSS.

# Answer: We need $ SM = ST $ (the third side equal)

### Problem 10: AAS
# Explanation:
## Step1: Recall AAS Criterion
AAS (Angle - Angle - Side) congruence requires two angles and a non - included side to be equal. In triangles $ \triangle KJL $ and $ \triangle UTS $, we know $ \angle K=\angle T $ (right angles) and $ KJ = UT $ (marked sides).
## Step2: Identify Missing Part
We need another pair of angles equal. For example, $ \angle L=\angle S $ (a non - included angle) to apply AAS.

# Answer: We need $ \angle L=\angle S $ (another pair of angles equal)

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QUESTION IMAGE

Question

Explanation:

Problem 6: ASA

Step1: Recall ASA Criterion

Step2: Identify Missing Part

Step1: Recall AAS Criterion

Step2: Identify Missing Part

Step1: Recall SAS Criterion

Step2: Identify Missing Part

Answer:

Problem 7: AAS