5 1 Quadrilaterals Quadrilateral Parallelogram More Parallelogram Characteristics

5. 1 Quadrilaterals

Quadrilateral: _____________ Parallelogram: ____________

More Parallelogram Characteristics Theorem 5. 1: ______________ Theorem 5. 2: ______________ Theorem 5. 3: ______________

Examples 6 y x 9 b 80 a x 12 y 9 a 2 b 45 35

3. Find the perimeter of parallelogram PINE if PI=12 and IN=8. P I 12 8 E N A B F D E G C

6. + 2 x 22 X=_______ 18 2 2 y- 4 7. 18 y=_______ X=_______ 11 x 4 y+5 80 Which to solve 1 st? 45 y=_______

True or False: 1. Every parallelogram is a quadrilateral? 2. Every Quad is a parallelogram? 3. All angles of a parallelogram are congruent? 4. All sides of a parallelogram are congruent? 5. In RSTU, RS is parallel to TU? 6. In XWYZ, XY=WZ ? 7. In ABCD, if angle A=50, then C=130?

5. 2 Proving Parallelograms

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 2 1 7 9 6 D 8 10 E 5 B 4 3 C

A 1 F 9 6 D 5 7 2 10 E 11 12 3 4 C 8 B

A 1 D 10 2 5 6 F E 8 7 4 B 9 3 C

5. 3 Parallel Lines

Theorems involving Parallel Lines Theorem 5. 8: ______________________________

C R, S, T are Midpoints. R A a) b) c) S T AB BC AC 12 14 15 18 22 B ST 5 TR RS 9 10 6

A R B S C T 1. If RS=12 then ST=_______ 2. If AB=8 then BC=____ 3. If AC=20 then AB=_______ 4. If AC=10 x then BC=______

C R, S, T are Midpoints. X A Z AB a) b) Y K 9 BC AC 8 24 6 B XY XZ 2 k+3 ZY

5. 4 Special Parallelograms

Special Parallelograms Rectangle: ______________ Rhombus: ______________ Square: _______________

Theorems for Special Parallelograms Theorem 5. 12: _____________________________ Theorem 5. 13: _____________________________ Theorem 5. 14: _____________________________

Proving a Rhombus or Rectangle Theorem 5. 16: ______________________________ Theorem 5. 17: ______________________________

Property Parallelogram Rect. Rhombus Square

Examples: ABCD is a Rhombus A 62 E D C B

M N 29 L P 12 O MNOP is a Rectangle

Y 2 3 X W 1 Z

A D B C 2 1 E

5. 5 Trapezoids

Warmup: Always, Never or Sometimes 1. A square is____ a rhombus. 2. The diagonals of a parallelogram _____ bisect the angles of a parallelogram. 3. The diagonals of a rhombus are _____ congruent. 4. A rectangle _____ has consecutive sides congruent. 5. The diagonals of a parallelogram are _____ perpendicular bisectors of each other

Trapezoid Theorems Theorem 5. 18: ____________________________

Solve: AB=10; DC=12 Find YW=_____ ZX=_____ XY=_____ 10 A Z D X Y 12 B W C

1. If AB=25, DC=13 then EF=_______ 2. If AE=11, FB=8 then AD=______ BC=______ 3. If AB=29 and EF=24 then DC=_____ 4. If AB=7 y+6, EF=5 y-3, and DC=y-5 then y=__ C F B D E A

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.