The "ABC DEF" naming convention does not directly refer to a specific congruence postulate in geometry. However, congruence postulates generally include Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA) among others. To determine which postulate applies, you would need to specify the relationships between the angles and sides of triangles ABC and DEF.
Yes, triangles ABC and DEF are congruent if all corresponding sides and angles are equal. The congruence postulate that applies in this case could be the Side-Angle-Side (SAS) postulate, which 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. Other applicable postulates include Side-Side-Side (SSS) and Angle-Angle-Side (AAS), depending on the known measurements.
To determine if triangle MNO is congruent to triangle PQR, we need to compare their corresponding sides and angles. If they are equal in length and measure, then MNO is congruent to PQR. The specific congruence postulate that could apply is the Side-Angle-Side (SAS) postulate, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
None; because there is no justification for assuming that the two triangles (or trangles, as you prefer to call them) are similar.
To determine if triangles PQR and XYZ are congruent, we need to compare their corresponding sides and angles. If all three pairs of sides are equal (SSS), or if two pairs of sides and the included angle are equal (SAS), or if two angles and the corresponding side between them are equal (ASA or AAS), then the triangles are congruent. Additionally, if the triangles are similar (AA), they may not be congruent unless their corresponding sides are also proportional. Thus, without specific measurements or angles provided, we cannot definitively conclude congruence.
Congruent - SSS
congruent - asa
congruent - SSSAnswer by Arteom, Friday December 10, 2010
Yes, triangles ABC and DEF are congruent if all corresponding sides and angles are equal. The congruence postulate that applies in this case could be the Side-Angle-Side (SAS) postulate, which 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. Other applicable postulates include Side-Side-Side (SSS) and Angle-Angle-Side (AAS), depending on the known measurements.
SAS
not congruent
Congruent - SAS
Might not be congruent
not congruent
similar - AA
To be congruent, the three angles of a triangle must be the same and the three sides must be the same. If triangles TRS and WUV meet those conditions, they are congruent.
yes