What defines a polygon in geometry?
A simple closed plane figure with three or more joined line segments.
What are the sides of a polygon?
The line segments that form the polygon.
What are vertices in a polygon?
The common endpoints of two sides.
What are interior angles of a polygon?
Angles formed inside the polygon.
How is a polygon with n sides commonly named?
It is called an n-gon.
What is the name of a polygon with three sides?
Triangle.
What is the name of a polygon with five sides?
Pentagon.
What is the name of a polygon with ten sides?
Decagon.
What is a convex polygon's interior angle property?
Every interior angle is less than 180°.
How do the vertices of a convex polygon point?
Its vertices point outward.
What interior angle property defines a concave polygon?
It has at least one interior angle greater than 180°.
How can the vertices of a concave polygon point?
Vertices can point inward and outward.
When is a polygon considered convex regarding side extensions?
If none of the extensions of its sides intersects the polygon.
When is a polygon considered concave regarding side extensions?
If any extension of its sides intersects the polygon.
What does joining one vertex to nonadjacent vertices in an n-sided polygon create?
It divides the polygon into n−2 non-overlapping triangles.
What is the formula for the sum of interior angles of an n-sided polygon?
S = (n−2) × 180°.
What is the interior-angle sum of a hexagon?
720°.
What is the number of sides if a polygon's interior-angle sum is 1080°?
8 sides.
What is an exterior angle of a convex polygon?
An angle outside the polygon formed by one side and the extension of an adjacent side.
What do the interior and adjacent exterior angles at a polygon vertex add to?
They add to 180°.
What is the sum of one exterior angle at each vertex of a convex n-sided polygon?
The sum is 360°.
What are the exterior angles corresponding to a triangle with interior angles 60°, 40°, and 80°?
They are 120°, 140°, and 100° respectively.
What defines a regular polygon?
It is both equiangular and equilateral.
What is the formula for each interior angle of a regular n-sided polygon?
(n-2)×180° divided by n.
How do you calculate each exterior angle of a regular n-sided polygon?
360° divided by n.
What is each interior angle of a regular pentagon?
108°.
What is each exterior angle of a regular pentagon?
72°.
What is a line of symmetry in a figure?
A line where two halves match exactly as mirror images.
How many lines of symmetry does an n-sided regular polygon have?
Exactly n lines of symmetry.
In an odd-sided regular polygon, what does each symmetry line connect?
A vertex to the midpoint of the opposite side.
In an even-sided regular polygon, what do symmetry lines connect?
Opposite vertices or opposite side midpoints.
When is a polygon inscribed in a circle?
When all its vertices lie on the circle.
When is a polygon circumscribed about a circle?
When each side touches the circle.
What is the circumcircle of a regular polygon?
The circle passing through all its vertices and centered at the polygon's center.
What is the apothem of a regular polygon?
The perpendicular segment from the center to the midpoint of a side.
What radius does the apothem represent in a regular polygon?
The radius of the incircle.
How do you calculate each central angle of a regular n-sided polygon?
By dividing 360° by n.
What is the formula for the side length of a regular n-gon inscribed in a circle?
s = 2r sin(180°/n).
How is the apothem of a regular n-gon with circumradius r calculated?
a = r cos(180°/n).
What is the formula for the perimeter of a regular n-gon inscribed in a circle?
P = 2nr sin(180°/n).
How do you calculate the area of a regular polygon using apothem and perimeter?
A = ½ a P.
What is the side length of a regular hexagon inscribed in a circle of radius r?
The side length is r.
What is the perimeter formula for a regular hexagon inscribed in a circle of radius r?
P = 6r.
What is the apothem of a regular hexagon inscribed in a circle of radius r?
a = (√3 / 2) r.
What is the area formula for a regular hexagon inscribed in a circle of radius r?
A = (3√3 / 2) r².
Test your knowledge with 20 questions on Regular Polygons.
1. A polygon has every interior angle measuring less than 180° and all of its vertices point outward. What type of polygon is it?
2. What does it mean for a line to be a line of symmetry of a figure?
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