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Which of the following is not a criterio...

Which of the following is not a criterion for congruence of triangle ?

A

SAS

B

ASA

C

SSA

D

SSS

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the following is not a criterion for the congruence of triangles, we need to analyze the options given: SAS, ASA, SSA, and SSS. ### Step-by-Step Solution: 1. **Understand the Criteria for Congruence of Triangles**: - **SAS (Side-Angle-Side)**: Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle. This is a valid criterion for congruence. - **ASA (Angle-Side-Angle)**: Two angles and the included side of one triangle are equal to two angles and the included side of another triangle. This is also a valid criterion for congruence. - **SSS (Side-Side-Side)**: All three sides of one triangle are equal to all three sides of another triangle. This is another valid criterion for congruence. - **SSA (Side-Side-Angle)**: Two sides and a non-included angle of one triangle are equal to two sides and a non-included angle of another triangle. This is **not** a valid criterion for congruence because it does not guarantee that the triangles are congruent. 2. **Identify the Incorrect Option**: - From the analysis, we see that SAS, ASA, and SSS are valid criteria for triangle congruence, while SSA is not. 3. **Conclusion**: - Therefore, the option that is not a criterion for congruence of triangles is **SSA**. ### Final Answer: The correct option is **SSA**.
To determine which of the following is not a criterion for the congruence of triangles, we need to analyze the options given: SAS, ASA, SSA, and SSS. ### Step-by-Step Solution: 1. **Understand the Criteria for Congruence of Triangles**: - **SAS (Side-Angle-Side)**: Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle. This is a valid criterion for congruence. - **ASA (Angle-Side-Angle)**: Two angles and the included side of one triangle are equal to two angles and the included side of another triangle. This is also a valid criterion for congruence. - **SSS (Side-Side-Side)**: All three sides of one triangle are equal to all three sides of another triangle. This is another valid criterion for congruence. ...
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    C
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    B
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    D
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