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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

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## 4.5, 4.6 and 4.8

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**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 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**Parallelogram Theorems**The opposite sides of a parallelogram are congruent The opposite angles of a parallelogram are congruent**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**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**Rectangle Theorems**A rectangle is a parallelogram (and so all parallelogram theorems apply The diagonals of a rectangle are congruent**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**Theorems of the Rhombus**A rhombus is a parallelogram (therefore, all parallelogram theorems apply) The diagonals of a rhombus are perpendicular**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**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**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**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**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!!**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**Practice Problems - Can You Do Them?**Are these shapes a parallelogram, rectangle, rhombus or none? Parallelogram, Rhombus None**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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