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JOURNAL 6..

JOURNAL 6. By: Nina Dorion. POLYGON. A polygon is a shape with straight sides, a polygon must have at least four angles and cannot have curved sides or an opened one. Polygon, straight sides. Not a polygon, has curved sides. Not a polygon, has one open side. Convex and concave polygons:.

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JOURNAL 6..

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  1. JOURNAL 6.. By: Nina Dorion

  2. POLYGON A polygon is a shape with straight sides, a polygon must have at least four angles and cannot have curved sides or an opened one Polygon, straight sides Not a polygon, has curved sides Not a polygon, has one open side.

  3. Convex and concave polygons: Convex: a polygon that has no angles pointing inwards, no internal angles can be more than 180. Concave: polygon that has internal angles greater than 180.

  4. CONVEX CONCAVE CONVEX CONCAVE

  5. EQUILATERAL AND EQUIANGULAR: equilateral means the sides are congruent Equiangular means the angles are congruent. 12 Equilateral Equiangular 12 12 12 equilateral

  6. INTERIOR ANGLES THEOREM FOR POLYGONS This theorem is used when you want to find the interior angles of a polygon, to do that you use this formula: (n-2)180 n For example: When you have a quadrilateral (four sides) you do the following: (4-2)180 fill in for n 4-2=2 (2)180=360 360/4=90 Each interior angle must be 900

  7. Pentagon 5-2=3 180x3=540 540/5=108 Each angle measures 1080 8-2=6 180x6=1080 1080/8=135 Each angle measures 135o Hexagon 6-2=4 180x4=720 720/6=120 Each angle measures 1200

  8. 4 theorems of parallelograms

  9. THEOREM: IF A QUADRILATERAL IS A PARALLELOGRAM, THEN ITS OPPOSITE ANGLES ARE CONGRUENT CONVERSE: IF BOTH PAIRS OF OPPOSITE ANGLES OF A QUADRILATERAL ARE CONGRUENT, THEN THE QUADRILATERAL IS A PARALLELOGRAM.

  10. EXAMPLES:

  11. THEOREM: If a quadrilateral is a parallelogram then its opposite sides are congruent. CONVERSE: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  12. EXAMPLES:

  13. THEOREM: If a quadrilateral is a parallelogram, then its diagonals bisect each other CONVERSE: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

  14. EXAMPLES:

  15. THEOREM: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. CONVERSE: If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram

  16. 45+135=180 45 135 67 88 92 67+113=180 88+92=180 113

  17. Prove that a quadrilateral is a parallelogram • Opposite sides are congruent • Opposite angles are congruent • Diagonals bisect each other • Consecutive angles are supplementary • One set of congruent and parallel sides • Opposite sides are parallel

  18. Opposite sides are congruent: Opposite angles are congruent:

  19. Diagonals bisect each other Consecutive angles are supplementary M<a+m<b=180 a b

  20. One set of congruent parallel sides Opposite sides are parallel

  21. Rectangle: A parallelogram with 4 right angles Diagonals are congruent

  22. Rhombus Parallelogram with 4 congruent sides

  23. Square Parallelogram that is both a rectangle and a rhombus 4 congruent sides and congruent angles Diagonals are congruent and perpendicular

  24. quadrilateral parallelogram rectangle rhombus square

  25. Trapezoid A quadrilateral with one pair of parallel sides Isosceles trapezoid: trapezoid with one pair of congruent legs A Properties of isosceles trapezoid: Diagonals are congruent Base angles congruent Opposite angles are supplementary B M<A+M<B=180

  26. base legs base

  27. Kite • has two pairs of congruent adjacent sides • Diagonals are perpendicular • One pair of congruent angles • One of the diagonals bisect the other

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