Polygons, Parallelograms, Rhombi, Squares, Kites, Trapezoids
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each of the black spaces below before clicking
on it to display the answer.
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| Rectangle | parallelogram with four right angles
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| 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
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| Rhombus | Rhombus is a parallelogram with 4 congruent sides
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| 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
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| 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.
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| Trapezoid | a quadrilateral with exactly one pair of parallel sides
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| isosceles trapezoid | trapezoid whose nonparallel sides are congruent
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| 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.
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| 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.
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| 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.
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| 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)
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| Polygons | a closed figure that has vertices, sides, angles and exterior angles.
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| How do you name a polygon? | By listing the vertices in order around the polygon.
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| Diagonal | a segment connecting 2 nonconsecutive vertices of a polygon.
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| Convex polygon | polygon where NO diagonal goes outside the figure
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| Concave polygon | Polygons where ANY diagonal goes outside the figure. Concave polygons "cave" in.
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| 3 sided polygon | triangle
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| 4 sided polygon | quadrilateral
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| 5 sided polygon | pentagon
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| 6 sided polygon | hexagon
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| 7 sided polygon | heptagon
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| 8 sided polygon | octagon
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| 9 sided polygon | nonagon
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| 10 sided polygon | decagon
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| 12 sided polygon | dodecagon
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| angle sums of polygons | number of triangles formed by diagonals from one vertex
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| interior angle sum theorem | the sum of the measures of the angles in a convex polygon with n sides is (n-2)180
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| exterior angle sum theorem | the sum of the measures of the exterior angles of ANY convex polygon, one at each vertex is 360.
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| 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.
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| Parallelogram | a quadrilateral with BOTH pairs of opposite sides parallel. Abbreviation: //gram
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| Properties of Parallelograms | opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other.
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| Theorem 6.9 | If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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| Theorem 6.10 | If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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| Theorem 6.11 | If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a //gram.
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| Theorem 6.12 | If one pair of opposite sides of a quadrilateral is BOTH congruent AND parallel, then the quadrilateral is a //gram.
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Created by:
amgeometry
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