Question

Which diagram matches the correct problem? A) Sketch an example of the ASA Congruence Postulate. B) Sketch an example of the SAS Congruence Postulate. C) Sketch an example of the AAS Congruence Theorem. D) Sketch an example of the SSS Congruence Postulate.

Answer 1

The student's question pertains to creating diagrams for different triangle congruence criteria, including ASA, SAS, AAS, and SSS, showing the necessary congruent parts for each criterion displayed in the sketches.

Step-by-step explanation:

The student is asking for sketches that exemplify different congruence postulates and theorems in geometry:

• ASA Congruence Postulate: Two triangles are congruent if two angles and the included side are equal in both triangles. In a sketch, you would show two triangles with two angles and the side between them marked as equal.
• SAS Congruence Postulate: Two triangles are congruent if two sides and the included angle are equal. In a corresponding diagram, two sides and the angle between them would be marked as congruent.
• AAS Congruence Theorem: Two triangles are congruent if two angles and a corresponding non-included side are equal. The sketch would depict two triangles with two angles and a non-included side marked as congruent.
• SSS Congruence Postulate: Two triangles are congruent if all three sides are equal. Accordingly, a diagram would show two triangles with all sides marked as congruent.

In each case, the correct diagram is dependent on accurately showing the claimed congruent parts as stated by the corresponding congruence criterion.