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5.1 Quadrilaterals. Quadrilateral :_________________________ Parallelogram : _______________________. More Parallelogram Characteristics. Theorem 5.1:____________________________ Theorem 5.2:___________________________ Theorem 5.3:___________________________. Examples. 6. y. x. 9. b.

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## 5.1 Quadrilaterals

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**Quadrilateral:_________________________**Parallelogram: _______________________**More Parallelogram Characteristics**Theorem 5.1:____________________________ Theorem 5.2:___________________________ Theorem 5.3:___________________________**Examples**6 y x 9 b 80 a x y 9 12 a 2b 45 35**3. Find the perimeter of parallelogram PINE if PI=12 and**IN=8. P I 12 8 N E A B F G D C E**6.**22 X=_______ y=_______ 2x+18 4y-22 18 7. X=_______ y=_______ 11x 4y+5 Which to solve 1st? 45 80**True or False:**• Every parallelogram is a quadrilateral? • Every Quad is a parallelogram? • All angles of a parallelogram are congruent? • All sides of a parallelogram are congruent? • In RSTU, RS is parallel to TU? • In XWYZ, XY=WZ ? • In ABCD, if angle A=50, then C=130?**Ways to Prove Quadrilaterals are Parallelograms**Theorem 5.4: _____________________________ ________________________________________ Theorem 5.5: _____________________________ ________________________________________ Theorem 5.6: _____________________________ ________________________________________**Theorem 5.7: _____________________**___________________________________ 5 ways to prove a quad is a Parallelogram 1. 2. 3. 4. 5.**A**B 1 7 2 8 9 10 E 6 3 4 5 D C**A**7 2 B 1 8 F 12 10 11 9 E 6 4 3 5 D C**A**E B 2 8 7 9 1 3 10 5 6 4 D F C**Theorems involving Parallel Lines**Theorem 5.8: _______________________ _____________________________________**Theorem 5.9: ____________________**__________________________________ __________________________________**Theorem 5.10: ______________________**____________________________________ ____________________________________**Theorem 5.11: ______________________**____________________________________ ____________________________________**C**R, S, T are Midpoints. R S A T B AB BC AC ST TR RS a) b) c) 12 14 18 15 22 10 5 9 6**A**R B S C T • If RS=12 then ST=_______ • If AB=8 then BC=________ • If AC=20 then AB=_______ • If AC=10x then BC=______**C**R, S, T are Midpoints. X Y A Z B AB BC AC XY XZ ZY a) b) K 24 2k+3 9 8 6**Special Parallelograms**Rectangle:___________________________ Rhombus:___________________________ Square: _____________________________**Theorems for Special Parallelograms**Theorem 5.12: ______________________ ___________________________________ Theorem 5.13:_______________________ ___________________________________ Theorem 5.14: _______________________ ___________________________________**Theorem 5.15: _____________________**___________________________________ ___________________________________**Proving a Rhombus or Rectangle**Theorem 5.16: _______________________ _____________________________________ _____________________________________ Theorem 5.17: _______________________ _____________________________________ _____________________________________**Examples:**ABCD is a Rhombus A B 62 E C D**M**N 29 MNOP is a Rectangle 12 L P O**Y**2 W 3 1 Z X**A**B 2 1 D E C**Warmup: Always, Never or Sometimes**• A square is________ a rhombus. • The diagonals of a parallelogram _________ bisect the angles of a parallelogram. • The diagonals of a rhombus are _________ congruent. • A rectangle _________ has consecutive sides congruent. • The diagonals of a parallelogram are _________ perpendicular bisectors of each other**Trapezoids**• Trapezoid: _______________________ • _____________________________________ • ________________________ • ________________________ • Isosceles Trapezoid _____________________ • ______________________________________**Trapezoid Theorems**Theorem 5.18:______________________ __________________________________**Theorem 5.19: ________________________**______________________________________ ______________________________________ ______________________________________**Solve: AB=10; DC=12**Find YW=_____ ZX=_____ XY=_____ 10 A B Z W X Y C D 12**If AB=25, DC=13 then EF=_______**• If AE=11, FB=8 then AD=______ BC=______ • If AB=29 and EF=24 then DC=_____ • If AB=7y+6, EF=5y-3, and DC=y-5 then y=__ C D F E A B**Find x=_______**y=_______ 4 x y**Quad TUNE is an isosiceles trapezoid with TU and NE as**bases. If angle U equals 62 degrees find the measures of the other 3 angles.

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