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Questions and Answers
If three sides of one triangle are equal to three sides of another triangle, what can be concluded about the triangles?
Which of the following is not a criterion for congruent triangles?
If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, what can be concluded about the triangles?
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, what can be concluded about the triangles?
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If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, what can be concluded about the triangles?
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Which criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent?
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Study Notes
Congruent Triangles
Criteria for Congruent Triangles
SSS Criterion (Side-Side-Side)
- If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
- This criterion ensures that the corresponding sides of the two triangles are equal.
ASA Criterion (Angle-Side-Angle)
- If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
- The included side is the side between the two given angles.
SAS Criterion (Side-Angle-Side)
- If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
- The included angle is the angle between the two given sides.
AAS Criterion (Angle-Angle-Side)
- If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
- The non-included side is a side that is not between the two given angles.
Note: These criteria are used to prove that two triangles are congruent, and they are all equivalent.
Congruent Triangles
Criteria for Congruent Triangles
SSS Criterion
- Three sides of one triangle are equal to three sides of another triangle, ensuring corresponding sides are equal.
ASA Criterion
- Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
- The included side is the side between the two given angles.
SAS Criterion
- Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
- The included angle is the angle between the two given sides.
AAS Criterion
- Two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.
- The non-included side is a side that is not between the two given angles.
General Notes
- These criteria are used to prove that two triangles are congruent.
- All four criteria (SSS, ASA, SAS, and AAS) are equivalent.
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Description
Understand the SSS and ASA criteria for congruent triangles, including the conditions for two triangles to be considered congruent.
