Diagram showing pairs of triangles to determine congruence using ASA and AAS theorems.
Two triangles in a diagram labeled with angles and sides, illustrating congruence using ASA and AAS criteria.
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Show Answer Key & Explanations
Step-by-step solution for: Solved Kota Software - Infinite Geometry Period Date SSS and ...
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Show Answer Key & Explanations
Step-by-step solution for: Solved Kota Software - Infinite Geometry Period Date SSS and ...
To determine if the two triangles in each pair are congruent using ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence, we need to analyze the given information for each pair of triangles. Let's go through each problem step by step.
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- Triangles: Two triangles are shown.
- Given Information: One angle and one side are marked as equal, but there is no clear indication of another angle being equal.
- Analysis: The given information does not satisfy either ASA or AAS because we do not have enough corresponding angles or sides marked as equal.
- Conclusion: The triangles are not congruent.
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- Triangles: Two right triangles are shown.
- Given Information: One angle (right angle) and two sides are marked as equal.
- Analysis: This satisfies the HL (Hypotenuse-Leg) congruence criterion for right triangles, which is a special case. However, since the question asks specifically about ASA or AAS, we cannot use HL here.
- Conclusion: The triangles are not congruent under ASA or AAS.
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- Triangles: Two triangles are shown.
- Given Information: Two angles and the included side are marked as equal.
- Analysis: This satisfies the ASA (Angle-Side-Angle) congruence criterion.
- Conclusion: The triangles are congruent by ASA.
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- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
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- Triangles: Two triangles are shown.
- Given Information: Two angles and a non-included side are marked as equal.
- Analysis: This satisfies the AAS (Angle-Angle-Side) congruence criterion.
- Conclusion: The triangles are congruent by AAS.
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- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
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- Triangles: Two triangles are shown.
- Given Information: Two angles and the included side are marked as equal.
- Analysis: This satisfies the ASA (Angle-Side-Angle) congruence criterion.
- Conclusion: The triangles are congruent by ASA.
---
- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
---
- Triangles: Two triangles are shown.
- Given Information: Two angles and a non-included side are marked as equal.
- Analysis: This satisfies the AAS (Angle-Angle-Side) congruence criterion.
- Conclusion: The triangles are congruent by AAS.
---
- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
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1. Not congruent
2. Not congruent
3. Congruent by ASA
4. Not congruent
5. Congruent by AAS
6. Not congruent
7. Congruent by ASA
8. Not congruent
9. Congruent by AAS
10. Not congruent
\boxed{1. \text{Not congruent}, 2. \text{Not congruent}, 3. \text{ASA}, 4. \text{Not congruent}, 5. \text{AAS}, 6. \text{Not congruent}, 7. \text{ASA}, 8. \text{Not congruent}, 9. \text{AAS}, 10. \text{Not congruent}}
---
Problem 1:
- Triangles: Two triangles are shown.
- Given Information: One angle and one side are marked as equal, but there is no clear indication of another angle being equal.
- Analysis: The given information does not satisfy either ASA or AAS because we do not have enough corresponding angles or sides marked as equal.
- Conclusion: The triangles are not congruent.
---
Problem 2:
- Triangles: Two right triangles are shown.
- Given Information: One angle (right angle) and two sides are marked as equal.
- Analysis: This satisfies the HL (Hypotenuse-Leg) congruence criterion for right triangles, which is a special case. However, since the question asks specifically about ASA or AAS, we cannot use HL here.
- Conclusion: The triangles are not congruent under ASA or AAS.
---
Problem 3:
- Triangles: Two triangles are shown.
- Given Information: Two angles and the included side are marked as equal.
- Analysis: This satisfies the ASA (Angle-Side-Angle) congruence criterion.
- Conclusion: The triangles are congruent by ASA.
---
Problem 4:
- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
---
Problem 5:
- Triangles: Two triangles are shown.
- Given Information: Two angles and a non-included side are marked as equal.
- Analysis: This satisfies the AAS (Angle-Angle-Side) congruence criterion.
- Conclusion: The triangles are congruent by AAS.
---
Problem 6:
- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
---
Problem 7:
- Triangles: Two triangles are shown.
- Given Information: Two angles and the included side are marked as equal.
- Analysis: This satisfies the ASA (Angle-Side-Angle) congruence criterion.
- Conclusion: The triangles are congruent by ASA.
---
Problem 8:
- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
---
Problem 9:
- Triangles: Two triangles are shown.
- Given Information: Two angles and a non-included side are marked as equal.
- Analysis: This satisfies the AAS (Angle-Angle-Side) congruence criterion.
- Conclusion: The triangles are congruent by AAS.
---
Problem 10:
- Triangles: Two triangles are shown.
- Given Information: One angle and two sides are marked as equal, but the angle is not between the two sides.
- Analysis: This satisfies the SAS (Side-Angle-Side) congruence criterion, but the question asks specifically about ASA or AAS. Since the angle is not between the two sides, it does not satisfy ASA or AAS.
- Conclusion: The triangles are not congruent under ASA or AAS.
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Final Answers:
1. Not congruent
2. Not congruent
3. Congruent by ASA
4. Not congruent
5. Congruent by AAS
6. Not congruent
7. Congruent by ASA
8. Not congruent
9. Congruent by AAS
10. Not congruent
\boxed{1. \text{Not congruent}, 2. \text{Not congruent}, 3. \text{ASA}, 4. \text{Not congruent}, 5. \text{AAS}, 6. \text{Not congruent}, 7. \text{ASA}, 8. \text{Not congruent}, 9. \text{AAS}, 10. \text{Not congruent}}
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