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Is ABC DEF If so name the congruence postulate that applies.?
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.
Is ABC trangle an trangle DEF If so name which similarity postulate or theorem applies.?
None; because there is no justification for assuming that the two triangles (or trangles, as you prefer to call them) are similar.
Is pqr congruent xyz if so name which similarity postulate or theorem applies?
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.
Is triangle uvw congruent to triangle xyz if so name the postulate that applies?
There is insufficient information for us to answer this question. Please edit the question to include more context or relevant information. We have no idea what triangles uvw and xyz are! It would also be useful to develop the habit of checking your questions for completeness before posting them.
What is the name of the postulate that states through any 3 points a circle can be formed?
There cannot be such a postulate because it is not true. Consider a line segment AB and let C be any point on the line between A and B. If the three points are A, B and C, there can be no circle that goes through them. It is so easy to show that the postulate is false that no mathematician would want his (they were mostly male) name associated with such nonsense. Well, if one of the points approach the line that goes through the other two points, the radius of the circle diverges. The line is the limit of the ever-growing circles. In the ordinary plane, the limit itself does not exist as a circle, but mathematicians have supplemented the plane with infinity to "hold" the centres of such "straight" circles.
