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| Define "polygon" - | A "polygon" is a plane figure that is formed by THREE OR MORE SEGMENTS called "sides", such that the following is true: (1) Each side intersects (connects with) exactly two other sides, once at each endpoint (2) No two sides with a common endpoint are "collinear (share the exact same space on the line)". |
| When is a polygon "convex" ? | A polygon is "convex" if no line that contains a side of the polygon contains a point in the interior of the polygon. |
| When is a polygon "nonconvex" or "concave" ? | A polygon is "nonconvex" or "concave" if it has a point in the interior of the polygon or it is NOT convex. |
| What are some of the "terms" that can be used to describe a polygon ? | Some of the "terms" that can be used to describe a polygon are the following: vertices (the point where two of the line segments (sides) of a polygon meet-their endpoints); interior (inside the area of the polygon); interior angles (angles inside of the polygon); exterior ("outside" of the interior area of a polygon); exterior angles (angles "outside" of the interior area polygon that are supplemental to the polygon's adjacent interior angle); perimeter (the measurement around the outer edge of the polygon; and, area (the measurement of the region within the polygon). |
| What is a "diagonal" of a polygon ? | A "diagonal" of a polygon is a segment that joints two "nonconsecutive vertices". |
| A "line segment" of a polygon must be at least one of what two things ? | A "line segment" of a polygon must be at least one of the following two things: (1) a SIDE (2) a DIAGONAL. |
| When is a polygon "equilateral" ? | A polygon is "equilateral" if all its sides are congruent (equal). |
| When is a polygon "equiangular" ? | A polygon is "equiangular" if all of its interior angles are congruent (equal). |
| When is a polygon "regular" ? | A polygon is "regular" of it is BOTH "equilateral" and "equiangular". |
| State Theorem 6.1 POLYGON INTERIOR ANGLES THEROEM - | Theorem 6.1 - POLYGON INTERIOR ANGLES THEOREM - The sum of the measures of the interior angles of a convex n-gon (n is the number of sides a given polygon has) is (n - 2)(180 degrees). |
| State the Corollary to Theorem 6.1 - | Collary to Theorem 6.1 - The measure of each interior angle of a REGULAR n-gon (n is the number of sides a polygon has) is 1/n(n - 2)(180 degrees). |
| State Theorem 6.2 - POLYGON EXTERIOR ANGLES THEOREM - | Theorem 6.2 POLYGON EXTERIOR ANGLES THEOREM - The sum of the measures of the exterior angles, one from each vertex, of a CONVEX polygon is 360 degrees. |
| State a the Corollary to Theorem 6.2 - | The Corollary to Theorem 6.2 - the measure of each exterior angle of a regular n-gon (n is the number of sides a polygon has) is 1/n(360 degrees). |
| State Theorem 6.3 - A PROPERTY OF A PARALLELOGRAM - | Theorem 6.3 A PROPERTY OF A PARALLELOGRAM - If a quadrilateral is a PARALLELOGRAMS, then its OPPOSITE SIDES are CONGRUENT. |
| State Theorem 6.4 - A PROPERTY OF PARALLELOGRAM - | Theorem 6.4 - A PROPERTIES OF PARALLELOGRAM - If a quadrilateral is a PARALLELOGRAM, then its OPPOSITE ANGLES are CONGRUENT. |
| State Theorem 6.5 A PROPERTY OF A PARALLELOGRAM - | Theroem 6.5 - A PROPERTY OF A PARALLELOGRAM - If a quadrilateral is a PARALLELOGRAM, then its CONSECUTIVE ANGLES are SUPPLEMENTARY. |
| State Theroem 6.5 - DIAGONALS OF A PARALLELOGRAM - | Theorem 6.6 - DIAGONALS OF A PARALLELOGRAM - If a quadrilateral is a PARALLELOGRAM, then its DIAGONALS BISECT each other. |
| State Theorem 6.7 - | Theorem 6.7 If BOTH PAIRS OF OPPOSITE SIDES of a quadrilateral are CONGRUENT, then the quadrilateral is a PARALLELOGRAM. |
| State Theorem 6.8 - | Theorem 6.8 - If BOTH PAIRS OF OPPOSITE ANGELS of a quadrilateral are CONGRUENT, then the quadrilateral is a PARALLELOGRAM. |
| State Therome 6.9 - | Theorem 6.8 - If AN ANGLE of a quadrilateral is SUPPLEMENTARY to both of its CONSECUTIVE ANGLES, then the quadrilateral is a PARALLELOGRAM. |
| State Theroem 6.10 - | Theorem 6.10 - If the DIAGONALS of a quadrilateral BISECT EACH OTHER, then the quadrilateral is a PARALLELOGRAM. |
| State Theorem 6.11 - | Theorem 6.11 - If ONE PAIR OF OPPOSITE SIDES of a quadrilateral are CONGRUENT AND PARALLEL, then the quadrilateral is a PARALLELOGRAM. |
| State Theorem 6.12 - | Theorem 6.12 - a PARALLELOGRAM is a RHOMBUS if and only if its DIAGONALS are PERPENDICULAR. |
| State Theorem 6.13 - | Theorem 6.13 - A PARALLELGRAM is a RHOMBUS if and only if each DIAGONAL BISECTS a PAIR OF OPPOSITE ANGLES. |
| State Theorem 6.14 - | Theoren 6.14 - A PARALLELOGRAM is a RECTANGLE if and only if is DIAGONALS are CONGRUENT. |
| State Theorem 6.15 - | Theorem 6.15 - A quardrilateral is a RHOMBUS if and only if it has FOUR CONFRUENT SIDES. |
| State Theorem 6.16 - | Theorem 6.16 - A quadrilateral is a RECTANGLE if and only if it has FOUR RIGHT ANGLES. |
