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Journal 6

Journal 6. Jaime Rich. Polygons:. A polygon is any closed shape with straight edges, or sides. Polygon Parts:. Side: a segment that forms a polygon Vertex: common endpoint of sides. Diagonal: segment that connects 2 non-consecutive vertices. EX:. a. a bcde is a polygon. b. c. d. e.

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Journal 6

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  1. Journal 6 • Jaime Rich

  2. Polygons: A polygon is any closed shape with straight edges, or sides. Polygon Parts: • Side: a segment that forms a polygon • Vertex: common endpoint of sides. • Diagonal: segment that connects 2 non-consecutive vertices.

  3. EX: a abcde is a polygon b c d e side a abc is a pollygon diagonal c b vertex

  4. Convex: • All vertices are pointing out • ALL regular polygons are convex Concave: • One ore more vertices are pointing in

  5. EX: Convex polygons Concave polygons

  6. Equilateral: • When all sides in a polygon are congruent Equiangular: • When all angles in a polygon are congruent

  7. EX: Equilateral Polygons Equiangular Polygons

  8. Interior Angle Theorem for Polygons: To know how to find the measure of the angles of a polygon you use this formula: (n-2)180. n stands for the number of sides each polygon has for example, a rectangle has 4 Sides so the formula is 4-2=2 times 180=360. The sum of all angles in a rectangle Is 360. To find the measure of each angle, divide the answer you get using the formula Above, by n, or the number of sides. For the rectangle it would be 360/4=90.

  9. EX: All angles (4-2)180=360 Each angle 360/4=90 All angles (5-2)180=540 Each angle 540/5=108 All angles (6-2)180=720

  10. Four Theorems of Parallelograms and Their Converse

  11. Theorems: 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. EX:

  13. Theorems: 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 quadriliateral is a parallelogram.

  14. EX:

  15. Theorems: 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.

  16. EX:

  17. Theorems: 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.

  18. EX: 130 110 120 50 70 60

  19. Proving Quadrilaterals are • Parallelograms: • Opposite angles are congruent • Opposite sides are congruent • Consecutive angles are supplementary • Diagonals bisect each other • Opposite sides are parallel • One set of congruent and parallel sides

  20. EX: 130 50 Congruent Opposite Angles Congruent sides Consecutive angles are supplementary Opposite sides are parallel. One set of congruent and parallel sides. Diagonals bisect each other

  21. Rectangle: A parallelogram with four right angles • Theorem: Diagonals are congruent

  22. EX:

  23. Square: A parallelogram that is both a rhombus and a rectangle. • Theorem: All four sides and all four angles are congruent Diagonals are congruent and perpendicular bisectors of each other

  24. EX:

  25. Rhombus: A parallelogram with four congruent sides • Theorem: Diagonals are perpendicular

  26. EX:

  27. Rectangle • Diagonals are congruent • 4 congruent • angles • Polygon • Quadrilateral • Parallelogram • Diagonals • bisect each other • Always regular polygon • Sort of mixture • between rhombus and • rectangle • Diagonals are perpendicular • 4 congruent sides Square Rhombus

  28. Trapezoid: A quadrilateral with a pair of parallel sides Isosceles trapezoid: one with a pair of congruent legs • Theorems: • Diagonals are congruent • Base angles are congruent (both sets) • Opposite angles are supplementary

  29. EX: Isosceles Trapezoid Both labeled angles are supplementary to each other.

  30. Kite: A quadrilateral with 2 different pairs of congruent sides. • Theorems: • Two pairs of congruent adjacent sides • Diagonals are perpendicular • One pair of congruent angles (the ones formed by the non-congruent sides) • One of the diagonals bisects the other diagonal

  31. EX:

  32. THE END!!!

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