Q: What is a polygon where all diagonals lie on its interior?

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It is a regular polygon as for example an equilateral triangle

A polygon which has a circumscribed circle is called a cyclic polygon.All regular simple polygons, all triangles and all rectangles are cyclic.

In a Frequency Polygon, a line graph is drawn by joining all the midpoints of the top of the bars of a histogram. A frequency polygon gives the idea about the shape of the data distribution. The two end points of a frequency polygon always lie on the x-axis.

Both alternate interior and alternate exterior angle pairs lie on opposite sides of the transversal.

adjacent angles.

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An interior angle is an angle defined by two sides of a polygon and that is inside the polygon. Opposite interior angles are specific pairs of interior angles, those that are opposite each other in the polygon. Alternate or opposite interior angles are also angles that lie on opposte sides of the tranversal line that cuts through parallel lines.

By definition, a regular polygon has all interior angles the same, but a concave polygon has some interior angles that are not identical. Also, it violates the axiom that all vertices lie on a circle.While it is possible to construct a polygon with equilateral sides, to be concave would require a form that is equally convex and laterally opposite. (An example is a 'solid arrow shape.')

A kite is a 4 sided quadrilateral and its 4 interior angles add up to 360 degrees, as in all quadrilaterals. The two diagonals lie at right-angles to each other.

It is a regular polygon as for example an equilateral triangle

A polygon which has a circumscribed circle is called a cyclic polygon.All regular simple polygons, all triangles and all rectangles are cyclic.

If, for any two points A and B in the polygon, all points with position A + kB are inside the polygon for 0 ≤ k ≤ 1, then the polygon is convex. In simple terms, if all points on the line AB lie inside the polygon, it is convex. If there is at least one point on AB that is outside the polygon then it is not a convex polygon.

No, a polygon must be 2 dimensional and lie on a single plane.

vertical lines

No interior angle of a convex polygon can exceed 180 degrees. A non-convex polygon has at least one reflex angle (> 180 degrees). Alternatively, a polygon is convex if, given any two points on or inside the polygon, the straight line joining the two points must lie wholly on or inside the polygon. In a non-convex polygon, it is possible to find a pair of points such that the straight line joining them lies outside the polygon for at least some of its length.

The center of mass of a rectangular lamina lies at the intersection of its diagonals. This point is equidistant from all four sides of the rectangle.

triangle

In a Frequency Polygon, a line graph is drawn by joining all the midpoints of the top of the bars of a histogram. A frequency polygon gives the idea about the shape of the data distribution. The two end points of a frequency polygon always lie on the x-axis.