Similar Triangles Worksheets - Free Printable

To determine whether each pair of triangles is similar, we need to use the properties of triangle similarity. Triangles are similar if they meet one of the following criteria:

1. AA (Angle-Angle) Similarity: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
2. SSS (Side-Side-Side) Similarity: If the corresponding sides of two triangles are proportional, then the triangles are similar.
3. SAS (Side-Angle-Side) Similarity: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

Let's analyze each pair of triangles step by step:

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Problem 1:

- Triangles: Two triangles with marked angles.
- Analysis: Both triangles have two pairs of congruent angles (marked with the same symbols).
- Conclusion: By the AA similarity criterion, these triangles are similar.
- Answer: Similar

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Problem 2:

- Triangles: Two triangles with side lengths labeled.
- Analysis: The side lengths of the triangles are proportional (e.g., 3:6 = 4:8 = 5:10).
- Conclusion: By the SSS similarity criterion, these triangles are similar.
- Answer: Similar

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Problem 3:

- Triangles: Two triangles with one angle marked and sides labeled.
- Analysis: The marked angles are congruent, and the sides around these angles are proportional (e.g., 2:4 = 3:6).
- Conclusion: By the SAS similarity criterion, these triangles are similar.
- Answer: Similar

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Problem 4:

- Triangles: Two triangles with no marked angles or proportional sides.
- Analysis: There is no clear indication of congruent angles or proportional sides.
- Conclusion: These triangles are not similar.
- Answer: Not Similar

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Problem 5:

- Triangles: Two triangles with one angle marked and sides labeled.
- Analysis: The marked angles are congruent, but the sides around these angles are not proportional (e.g., 3:6 ≠ 4:5).
- Conclusion: These triangles do not satisfy the SAS similarity criterion.
- Answer: Not Similar

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Problem 6:

- Triangles: Two triangles with all three angles marked as congruent.
- Analysis: All three angles of one triangle are congruent to the corresponding angles of the other triangle.
- Conclusion: By the AA similarity criterion, these triangles are similar.
- Answer: Similar

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Problem 7:

- Triangles: Two triangles with side lengths labeled.
- Analysis: The side lengths of the triangles are proportional (e.g., 5:10 = 7:14 = 9:18).
- Conclusion: By the SSS similarity criterion, these triangles are similar.
- Answer: Similar

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Problem 8:

- Triangles: Two triangles with one angle marked and sides labeled.
- Analysis: The marked angles are congruent, and the sides around these angles are proportional (e.g., 4:8 = 5:10).
- Conclusion: By the SAS similarity criterion, these triangles are similar.
- Answer: Similar

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Final Answers:

1. Similar
2. Similar
3. Similar
4. Not Similar
5. Not Similar
6. Similar
7. Similar
8. Similar

Boxed Answer:
\[
\boxed{\text{Similar, Similar, Similar, Not Similar, Not Similar, Similar, Similar, Similar}}
\]