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Q: Is pqr similar xyz if so name which similar postulate or Therom applies?
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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 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.


What 4 US states have a vertical line of symmetry?

Ohio Hawaii The symmetry applies to the name of the state when it is written vertically, not to the state itself. And also, who normally writes the name of anything vertically?


What polygon is similar to every other polygon of the same name?

square and rhombus