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J O U R N A L 6

J O U R N A L 6. Maria Elisa Vanegas 9-5. Polygons. Parallelograms. *Interior & Exterior Angles. * Theorems * Quadrilaterals. R ectangle. Trapezoid. Rhombus. * I sosceles. Square. Polygon. A Polygon is a closed figure that is formed by 3 or more straight segments. Vocab:

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J O U R N A L 6

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  1. JOURNAL6 Maria Elisa Vanegas 9-5

  2. Polygons Parallelograms *Interior & Exterior Angles *Theorems *Quadrilaterals Rectangle Trapezoid Rhombus *Isosceles Square

  3. Polygon APolygonis a closed figure that is formed by 3 or more straight segments. Vocab: Sides of a Polygon= segment that forms a polygon. Vertex of the Polygon= common endpoints of 2 sides. Diagonal= a segment that connects any 2 non consecutive vertices. Equilateral= a polygon with all equal sides. Equiangular= a polygon with all equal angles. CONCAVE Any figure that has 1 or more vertex pointing in. CONVEX Any figure that has all vertexes pointing out. REGULAR is one that is both equilateral and equiangular. ≠ regular = irregular

  4. Polygons Concave & Convex Regular & Irregular

  5. Interior Angle theorem for Polygons= (n-2) x 180 By using this formula you will be able to found the sum of all the interior angles added together. If you want to find each interior angle then you divide the answer by the number of sides.

  6. Exterior Angle Sum theorem for Polygons= For all polygons the sum of the exterior angles is ALWAYS going to add up to 360⁰. If you want to find out each exterior angle then you divide the number of sides by 360.

  7. parallelogram AParallelogramis a quadrilateral that has opposite sides parallel to each other OR it has 2 pairs of parallel sides. A Quadrilateral can be a Parallelogram if it has the following properties… Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other 2 pairs of parallel sides One set of congruent and parallel sides

  8. Parallelogram Theorems If a quadrilateral is a parallelogram then… Opposite sides are congruent. Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other Converse… If the opposite sides of a quadrilateral are congruent then it is a parallelogram. If the opposite angles in a quadrilateral are congruent then it is a parallelogram. If the consecutive angles in a quadrilateral are supplementary then it is a parallelogram. If the diagonals in a quadrilateral bisect each other then it is a parallelogram.

  9. rectangle A Rectangle is any parallelogram with 4 right angle. Its diagonals are congruent.

  10. rhombus A Rhombus is a parallelogram with 4 congruent sides, in which its diagonals are perpendicular.

  11. square A Square is a parallelogram that is both a rectangle and a rhombus. So it has 4 right angles, 4 congruent sides and angles, and its diagonals are perpendicular and congruent.

  12. Trapezoid >> Trapezoid= A quadrilateral with one pair of parallel sides. >> Isosceles Trapezoid= is a trapezoid with a pair of congruent angles. Properties of an Isosceles Trapezoid Diagonals are congruent Base angles (both sets) are congruent Opposite angles are supplementary Midsegment Theorem Midsegment= (b1+ b2) / 2 It is parallel to both bases It takes the same distance getting from base 1 to the midsegment and from the midsegment to base 2.

  13. Isosceles Trapezoid

  14. Midsegment

  15. kite Kite= A quadrilateral that has 2 pairs of congruent adjacent sides (2 lines at the top are congruent and the 2 lines at the bottom are congruent) Properties of a kite Diagonals are perpendicular One of the diagonals bisect the other One pair of congruent angles (the ones formed by the non-congruent sides)

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