Question

1. how are the following triangle congruent? if they are not congruent then choose nei (not enough information or not possible)

side - side - side
side - angle - side
angle - side - angle

Explanation:

Step1: Recall congruence criteria

Side - Side - Side (SSS) means all three sides of one triangle are equal to the corresponding three sides of another triangle. Side - Angle - Side (SAS) means two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle. Angle - Side - Angle (ASA) means two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

Step2: Analyze first row

Since no side - length or angle - measure information is given, we choose NEI.

Step3: Analyze second row

Again, without side - length or angle - measure information, we choose NEI.

Step4: Analyze third row

If the marked sides are equal as shown, and assuming the un - marked sides are also equal based on the markings, we have SSS.

Step5: Analyze fourth row

If the marked side is common, and the marked angles and sides match as shown, we have SAS.

Answer:

1st row: NEI
2nd row: NEI
3rd row: Side - Side - Side
4th row: Side - Angle - Side