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# 4.5, 4.6 and 4.8

4.5, 4.6 and 4.8. By Tamago and Faris. Today’s Special: QUADRILATERALS!. Quadrilateral – a polygon with four sides Parallelogram – a quadrilateral with two pairs of parallel sides Kite – a quadrilateral with exactly two pairs of adjacent congruent sides

## 4.5, 4.6 and 4.8

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### Presentation Transcript

1. 4.5, 4.6 and 4.8 By Tamago and Faris

2. Today’s Special:QUADRILATERALS! Quadrilateral – a polygon with four sides Parallelogram – a quadrilateral with two pairs of parallel sides Kite – a quadrilateral with exactly two pairs of adjacent congruent sides Rectangle – a quadrilateral with four right angles Rhombus – a quadrilateral with four congruent sides Square – quadrilateral with four congruent sides and angles. Trapezoid – a quadrilateral with one and only one pair of parallel sides

3. Parallelogram Theorems The opposite sides of a parallelogram are congruent The opposite angles of a parallelogram are congruent

4. Parallelogram Diagonal Theorems A diagonal of a parallelogram divides the parallelogram into two congruent triangles The diagonals of a parallelogram bisect each other            A                                               B C                                              D

5. OMG, I donno if this is a parallelogram!! It's a parallelogram... If two pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

6. Rectangle Theorems A rectangle is a parallelogram (and so all parallelogram theorems apply The diagonals of a rectangle are congruent

7. Is It a Rectangle? More Theorems If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle Housebuilder Theorem If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

8. Theorems of the Rhombus A rhombus is a parallelogram (therefore, all parallelogram theorems apply) The diagonals of a rhombus are perpendicular

9. Help me! I cannot identify this shape as a rhombus! If one pair of adjacent sides of a parallelogram are congruent, then the quadrilateral is a rhombus If the diagonals of a parallelogram bisect the angles of a parallelogram, then the parallelogram is a rhombus If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

10. We need squares… NOW!!!! A square is a rectangle (so all theorems of rectangles apply) A square is a rhombus (and all theorems of rhombi apply) The diagonals of a square are congruent and are the perpendicular bisectors of each other

11. Random Kite Slide and Bad Grammar The diagonals of a kite are perpendicular BETWEENNESS POSTULATE Given points P, Q and R, is PQ + QR = PR, then Q is between P and R on a line P Q R

12. Theorems for Triangles! TRIANGLE MIDSEGMENT THEOREM A midsegment of a triangle is parallel to a side of a triangle and its length is equal to half the length of that side TRIANGLE INEQUALITY THEOREM The sum of the length of any two sides of a triangle is greater than the length of the third side

13. Interesting Facts that May Catch Your Attention so You Don’t Fall Asleep… or Maybe Not. The plural of rhombus can either be rhombi OR rhombuses Fun little website about rhombi: OMFSM CLICK ME!!

14. Let’s Prove Some Theorems! Def. of parallelogram A diagonal of a parallelogram divides the parallelogram into two congruent triangles Given: parallelogram PLGM with diagonal Prove: Alt. int. angles Def. of parallelogram Alt. int. angles Reflexive ASA

15. Practice Problems - Can You Do Them? Are these shapes a parallelogram, rectangle, rhombus or none? Parallelogram, Rhombus None

16. 5 60° 40° 7.7 7 5 50° Practice Problems - Can You Do Them? Find the indicated measures. Assume both are parallelograms 5 80°

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