1. **Problem Statement:** Illustrate the given Euclidean geometry concepts about points, lines, angles, and triangles. 2. **Euclidean Geometry Illustration Explanation:** - Two collinear points determine a line that extends infinitely in both directions. - Three collinear points have one point between the other two. - A line segment is the shortest path between two points. - Two coplanar lines intersect at a point forming four angles. - Given a line and a point not on it, exactly one parallel line passes through that point. - Perpendicular lines intersect forming four right angles. - Three non-collinear points form a triangle. - The sum of interior angles in a triangle is 180 degrees. - A triangle can have one right or obtuse angle. - An equiangular triangle has all angles equal to 60 degrees. 3. **Spherical Geometry Statement:** On a sphere: - "Lines" are great circles. - Two points determine a great circle arc, the shortest path on the sphere. - Three points on a great circle are collinear on the sphere. - The sum of interior angles of a triangle exceeds 180 degrees. - There are no parallel lines; all great circles intersect. - Perpendicular great circles intersect at right angles. 4. **Spherical Geometry Illustration Explanation:** - Great circles intersect in two antipodal points. - Triangles formed by arcs of great circles have angle sums greater than 180 degrees. 5. **Summary:** Euclidean geometry deals with flat planes and straight lines, while spherical geometry deals with curved surfaces where lines are great circles and angle sums differ.