Yes, they do exist. And the question is ... ?
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Triangles do not have parallel lines but as right angles triangles they do have perpendicular lines that meet at 90 degrees.
Yes they have straight lines no curves and angles.
Yes, draw the lines from the obtuse angles to the center of the line opposite from it.
It started off as a study of triangles and is a study of straight lines and angles, as well as relationships between them.
Similar triangles don't just have proportional angles, they have IDENTICAL angles!