1. Prove the nature of the vertical line in the line segment: Penseri closure theorem can be used to prove that the distance between a point on the vertical line in the line segment and the two endpoints of the line segment is equal. This property is very useful in solving problems related to the median perpendicular of a line segment.
2. Prove the nature of an angle: Penseri's closure theorem can be used to prove that the complementary angle of an angle is equal to its antipodal angle. This property is very useful in solving problems related to the properties of angles.
3. Prove the nature of triangle: Penseri's closure theorem can be used to prove that the complementary angle of one internal angle of triangle is equal to the sum of the other two internal angles. This property is very useful in solving problems related to the properties of triangles.
4. Prove the nature of parallel lines: Poncelet's closure theorem can be used to prove that the included angle between two parallel lines is equal. This property is very useful in solving problems related to the properties of parallel lines.
5. Prove the nature of a circle: Poncelet's closure theorem can be used to prove that the distance from a point on a circle to the center of the circle is equal to the distance from that point to any point on the circle. This property is very useful in solving problems related to the properties of circles.
In a word, Poncelet's closure theorem is widely used in high school mathematics, which can be used to prove many geometric properties and help us better understand and solve geometric problems.