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Chapter 6
Polygons, Parallelograms, Rhombi, Squares, Kites, Trapezoids
| Term | Definition |
|---|---|
| Rectangle | parallelogram with four right angles |
| Properties of a Rectangle | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are congruent, opposite sides are parallel, 4 right angles |
| Rhombus | Rhombus is a parallelogram with 4 congruent sides |
| Properties of a Rhombus | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are perpendicular; diagonals bisect each pair of opposite angles. DIAGONALS ARE NOT CONGRUENT |
| Properties of a Square | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are congruent; diagonals are perpendicular; diagonals bisect each pair of opposite angles. |
| Trapezoid | a quadrilateral with exactly one pair of parallel sides |
| isosceles trapezoid | trapezoid whose nonparallel sides are congruent |
| Properties of a Trapezoid | angles along the leg add to 180 degrees; all four angles add to 360 degrees; if the trapezoid is isosceles, then the base angles are equal and the diagonals are congruent. |
| Kite | a kite is a quadrilateral with two pairs of consecutive sides congruent and NO opposite sides congruent. A kite has NO parallel sides, so a kite is NOT a parallelogram. |
| Properties of a Kite | all four angles add up to 360 degrees; diagonals are perpendicular; one pair of opposite angles are congruent; no parallel sides. At the short diagonal, the angles are congruent. At the long diagonal, the diagonals are bisected. |
| Trapezoid Midsegment Theorem | The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. M=1/2 (base one + base two) |
| Polygons | a closed figure that has vertices, sides, angles and exterior angles. |
| How do you name a polygon? | By listing the vertices in order around the polygon. |
| Diagonal | a segment connecting 2 nonconsecutive vertices of a polygon. |
| Convex polygon | polygon where NO diagonal goes outside the figure |
| Concave polygon | Polygons where ANY diagonal goes outside the figure. Concave polygons "cave" in. |
| 3 sided polygon | triangle |
| 4 sided polygon | quadrilateral |
| 5 sided polygon | pentagon |
| 6 sided polygon | hexagon |
| 7 sided polygon | heptagon |
| 8 sided polygon | octagon |
| 9 sided polygon | nonagon |
| 10 sided polygon | decagon |
| 12 sided polygon | dodecagon |
| angle sums of polygons | number of triangles formed by diagonals from one vertex |
| interior angle sum theorem | the sum of the measures of the angles in a convex polygon with n sides is (n-2)180 |
| exterior angle sum theorem | the sum of the measures of the exterior angles of ANY convex polygon, one at each vertex is 360. |
| regular polygons | a polygon that is BOTH equilateral and equiangular. IF you see the word regular with a polygon, you can divide by the number of sides to find the individual angle measures. |
| Parallelogram | a quadrilateral with BOTH pairs of opposite sides parallel. Abbreviation: //gram |
| Properties of Parallelograms | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other. |
| Theorem 6.9 | If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. |
| Theorem 6.10 | If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. |
| Theorem 6.11 | If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a //gram. |
| Theorem 6.12 | If one pair of opposite sides of a quadrilateral is BOTH congruent AND parallel, then the quadrilateral is a //gram. |
Created by:
amgeometry
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