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Journal chapter 6

BY: Amani Mubarak 9-5. Journal chapter 6. POLYGON. A polygon is a closed figure with connected straight line segments . Depending on how many sides the polygon has, it will be given its name . PARTS OF A POLYGON. Each polygon includes 3 different sides : * Side - each segment

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Journal chapter 6

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  1. BY: Amani Mubarak 9-5 Journalchapter 6

  2. POLYGON • A polygon is a closed figure withconnectedstraight line segments. • Dependingonhowmanysidesthepolygon has, itwillbegivenitsname.

  3. PARTS OF A POLYGON • Eachpolygonincludes 3 differentsides: *Side- each segment *vertex- commonendpoints of twopoints *diagonal- segment thatconnectsanytwononconsecutivevertices. side vertex side diagonal diagonal diagonal side vertex vertex

  4. CONVEX AND CONCAVE POLYGONS • In orderto determine if a polygon is eitherconcaveorconvextheonlythingyouneedtoknow is thatconcavepolygons are theonesthathaveatleastonevertexpointinginside. Toknowifit is a convex, all of thevertexesmustbepointingout. EXAMPLES: convex convex concave concave

  5. EQUILATERAL AND EQUIANGULAR POLYGONS • Every regular polygon is bothequilateral and equiangular. A polygon is equilateralwhenallsides are congruent, and equiangularwhenallangles are congruent.

  6. INTERIOR ANGLE THEOREM FOR POLYGONS • The sum of the interior anglemeasures of a convexpolygonwith n sides is (n-2)180° P (3-2)180° 1X180=180 180÷3= 34.3 c° Q 3c° (4-2)180° 2X180=360 C +3c+c+3c= 360 8c=360 C=45 Angle P and R= 45° Angle S and Q= 135° 3c° c° S (4-2)180° 2X180= 360 360÷4=90 R

  7. PARALLELOGRAMS 4 Theorems Theorem 6-2-1 • If a quadrilateral is a parallelogram, then its opposite sides are congruent. converse: If the opposite sides of a quadrilateral are congruent, then it is a parallelogram. Theorem 6-2-2 • If a quadrilateral is a parallelogram, then its opposite angles are congruent. Converse:If the opposite angles of a quadrilateral are congruent, then it is a parallelogram.

  8. Theorem 6-2-3 • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Converse:If the consecutive angles of a quadrilateral are supplementary, then it is a quadrilateral. Theorem 6-2-4 • If a quadrilateral is a parallelogram, then its diagonals bisect each other. Converse: If the diagonals of a quadrilateral bisect each other then it is a parallelogram.

  9. Howtoprove a quadrilateral is a parallelogram • In ordertoprove a quadrilateral is parallelogramyoumustknowthefollowingproperties: • Oppositesides are congruent and parallel. • Oppositeangles are congruent • Consecutiveangles are supplementary • Diagonalsbisecteachother • One set of congruent and parallelsides

  10. Theoremsthatprovequadrilateral is parallelogram: • PROPERTIES OF RECTANGLES • 6-4-1: if a quadrilateral is a rectangle, thenit is a parallelogram. • 6-4-2: if a parallelogram is a rectangle, thenitsdiagonals are congruent.

  11. PROPERTIES OF RHOMBUSES • 6-4-3: if a quadrilateral is a rhombus, then ir is a parallelogram. • 6-4-4: if a parallelogram is a rhombus, thenitsdiagonals are perpendicular. • 6-4-5: if a parallelogramis a rhombus, theneach diagonal bisects a pair of oppositeangles.

  12. Rhombus, Square, Rectangle • Rectangle is a parallelogramwith 4 rightangles. Diagonals are congruent. • Rhombus is a parallelogramwithfourcongruentsides. Diagonals are perpendicular. • Square is a parallelogramthat is both a rectangle and a rhombus. Itsfoursides and angles are congruent. Diagonals are congruent and perpendicular. • Whatthisthree figures have in common is thatthey are allparallelograms, and havefoursides.

  13. More examples…

  14. RectangleTheorems • Theorem 6-5-1 Ifoneangle of a parallelogram is a rightangle, thentheparallelogram is a rectangle. • Theorem 6-5-2 Ifthediagonals of a parallelogram are congruent, thentheparallelogram is a rectangle. C B D E A D DGcongruentFE F G

  15. RhombusTheorems • Theorem 6-5-3 Ifonepair of consecutivesides of a parallelogram are congruent, thentheparallelogram is a rhombus. • Theorem 6-5-4 Ifthediagonals of a parallelogram are perpendicular, thentheparalellogram is a rhombus. • Theorem 6-5-5 Ifone diagonal of a parallelogrambisects a pair of oppositeangles, thetheparallelogram is a rhombus.

  16. Trapeziod • A trapezoid is a quadrilateralwithonepair of parallelsides. • Isosceles is a trapezoidwith a pair of congruentlegs. • Diagonals are congruent • Base angles (both sets) are congruent • Oppositeangles are supplementary.

  17. TrapezoidTheorems • 6-6-3: if a quadrilateral is anisoscelestrapezoid, theneachpair of base angles are congruent. • 6-6-4: if a trapezoid has onepair of congruent base angles, thenthetrapezoid is isosceles. • 6-6-5: a trapezoid is isoscelesif and onlyifitsdiagonals are congruent.

  18. Kite • A kite is made up of: • Twopairs of congruentadjacentsides. • Diagonals are perpendicular • Onepair of congruentangles. • One of thediagonalsbisectstheother.

  19. KiteTheorems • 6-6-1: if a quadrirateral is a kite, thenitsdiagonals are perpendicular. • 6-6-2: if a quadrilateral is a kite, thenexactlyonepair of oppositeangles are congruent.

  20. _____(0-10 pts.) Describe what a polygon is. Include a discussion about the parts of a polygon. Also compare and contrast a convex with a concave polygon. Compare and contrast equilateral and equiangular. Give 3 examples of each. _____(0-10 pts.) Explain the Interior angles theorem for polygons. Give at least 3 examples. _____(0-10 pts.) Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each. _____(0-10 pts.) Describe how to prove that a quadrilateral is a parallelogram.  Give at least 3 examples of each. _____(0-10 pts.) Compare and contrast a rhombus with a square with a rectangle. Describe the rhombus, square and rectangle theorems. Give at least 3 examples of each. _____(0-10 pts.) Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each. _____(0-10 pts.) Describe a kite. Explain the kite theorems. Give at least 3 examples of each.

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