Worksheet for identifying congruent triangles using ASA and AAS criteria.

I'll solve this problem by analyzing the pairs of triangles to determine if they are congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria.

Let me examine each pair one by one:

First, I need to understand what ASA and AAS mean:
- ASA: Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
- AAS: Two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle.

Now let me analyze each pair:

Pair 1 (top left):
- Looking at the markings, I can see that two angles are marked as congruent (with single and double arcs), and the side between them is also marked as congruent.
- This satisfies the ASA criterion.
- So these triangles are congruent by ASA.

Pair 2 (top right):
- I can see two angles marked as congruent (single and double arcs), and a side that is not between these two angles is also marked as congruent.
- This satisfies the AAS criterion.
- So these triangles are congruent by AAS.

Pair 3 (middle left):
- I can see two angles marked as congruent (single and double arcs), and the side between them is also marked as congruent.
- This satisfies the ASA criterion.
- So these triangles are congruent by ASA.

Pair 4 (middle right):
- I can see two angles marked as congruent (single and double arcs), and a side that is not between these two angles is also marked as congruent.
- This satisfies the AAS criterion.
- So these triangles are congruent by AAS.

Pair 5 (bottom left):
- I can see two angles marked as congruent (single and double arcs), and the side between them is also marked as congruent.
- This satisfies the ASA criterion.
- So these triangles are congruent by ASA.

Pair 6 (bottom right):
- I can see two angles marked as congruent (single and double arcs), and a side that is not between these two angles is also marked as congruent.
- This satisfies the AAS criterion.
- So these triangles are congruent by AAS.

Based on my analysis, all six pairs of triangles are congruent. The first, third, and fifth pairs are congruent by ASA, while the second, fourth, and sixth pairs are congruent by AAS.

The handwritten answers in the image appear to match my analysis:
- Pair 1: ASA ✓
- Pair 2: AAS ✓
- Pair 3: ASA ✓
- Pair 4: AAS ✓
- Pair 5: ASA ✓
- Pair 6: AAS ✓

All the answers provided in the image are correct according to the ASA and AAS congruence criteria.