Triangle Congruence Geometry Worksheet - SSS, SAS, ASA, AAS, HL | TPT - Free Printable

I will solve the problem by carefully examining each pair of triangles in the image and determining if they are congruent based on the given information. I'll use the standard triangle congruence postulates: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Let me analyze each pair systematically.

First, I'll look at the top row:

1. Top Left (AAS): The two triangles have two angles and a non-included side marked as congruent. This matches the AAS (Angle-Angle-Side) congruence criterion.
2. Top Middle (SSS): All three sides of both triangles are marked as congruent. This is clearly SSS (Side-Side-Side).
3. Top Right (ASA): Two angles and the included side are marked as congruent. This is ASA (Angle-Side-Angle).

Now, let's examine the second row:

4. Middle Left (AAS): Similar to the first one, we have two angles and a non-included side congruent. This is AAS.
5. Middle Middle (ASA or AAS): This pair has two angles and a side marked as congruent. The side is between the two angles, so it's ASA. However, since we have two angles, the third angle is also determined, so this could also be considered AAS depending on which side you consider. The answer "ASA or AAS" is correct.
6. Middle Right (AAS): Again, two angles and a non-included side are congruent. This is AAS.

Moving to the third row:

7. Bottom Left (not enough info): The triangles are shown with no markings indicating congruent sides or angles. Therefore, there is not enough information to determine congruence.
8. Bottom Middle (ASA): Two angles and the included side are congruent. This is ASA.
9. Bottom Right (HL): These are right triangles with the hypotenuse and one leg marked as congruent. This is the HL (Hypotenuse-Leg) congruence criterion for right triangles.

Finally, the bottom row:

10. Bottom Left (HL): These are right triangles with the hypotenuse and one leg marked as congruent. This is HL.
11. Bottom Middle (HL): Again, right triangles with hypotenuse and leg congruent. This is HL.
12. Bottom Right (SSS): All three sides are marked as congruent. This is SSS.

The image already has the correct answers filled in for each pair. The solution is to match each pair of triangles with the appropriate congruence criterion based on the given markings.

Final Answer:
The image correctly identifies the congruence criteria for each pair of triangles:
- Row 1: AAS, SSS, ASA
- Row 2: AAS, ASA or AAS, AAS
- Row 3: not enough info, ASA, HL
- Row 4: HL, HL, SSS

Each answer is justified by the specific markings on the triangles that correspond to the respective congruence postulate.