Download Unit 4 Note Packet

Name:_____________________________
Unit 4: Properties of Polygons
4.1 Parallelograms
4.2 Rectangles
4.3 Squares/ Rhombi
4.4 Trapezoids and Kites
4.5 2-Column Proofs
GEOMETRY Unit 4, Quadrilaterals
Notes 4-1, Parallelograms
Parallelograms
Name ________________________
Date __________ Period _________
(Note: All quadrilaterals in this set of notes are parallelograms.)
A parallelogram is a quadrilateral with both pairs of opposite
sides parallel.
(Mark the parallel sides of parallelogram ABCD)
Draw a picture to illustrate
your conjecture
Parallelogram Conjecture #1
(6-1) :
Opposite sides of a parallelogram are __________________
Ex 1: Solve for x and y.
Ex 2: Solve for x and y.
Ex 3: Solve for x and find AB.
Draw a picture to illustrate
your conjecture
Parallelogram Conjecture #2
(6-2)
Opposite angles of a parallelogram are ______________.
Ex 4: Solve for x and y.
Ex 5: Solve for x
Ex 6: Solve for x and y
& find m D .
& find m C and m D .
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Draw a picture to illustrate
your conjecture
Parallelogram Conjecture #3
(6-3):
Consecutive angles of a parallelogram are _______________.
Ex 7: If mA  115  , find mB , mC and mD .
Ex 8: Solve for x and find mC .
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Ex 9: Find mA and mD .
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Parallelogram Conjecture #4
(6-4):
The diagonals of a parallelogram ____________________
Ex 10: If AE = 8, find EC.
Ex 11: If EB = 12 and DE = 3x, solve for x.
Ex 12: If DE = 7x + 2 and EB = 9x – 6, find DB.
Ex 13: If EC = 3x – 8 and AC = 4x +6,
solve for x and find AC.
Ex 14: Solve for x.
Ex 15: Solve for x and y.
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GEOMETRY Unit 4, Quadrilaterals
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Notes 4-2, Rectangles
Rectangles

Name ________________________
Date __________ Period _________
Determine if the quadrilateral with the given vertices is a parallelogram.
R (1, 1), S (3, 6), T (9, 8) and V (7, 3)
Definition of a rectangle -

Determine if the quadrilateral with the given vertices is a rectangle.
R (2, 2), S (0, 6), T (6, 9) and V (8, 5)
Note that a rectangle is a special type of __________________________. Therefore, a
rectangle has the following properties:
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Property
Why does it have this property?
1.
2.
3.
4.
5.
Rectangle Conjecture #1
(6-9):
Use rectangle ABCD to answer the following (treat each question independently):
1. If EB = 12, then AE = _______
2. If EC = 12x – 4 and DE = 44, then x = _______
3. If AE = 5x – 2 and DB = 6x + 16, then AC = _______
4. If mEAD  49  , then mAED = ______ and mAEB = _______
Use rectangle ABCD to answer the following questions:
5. If m1  43 and m3  13x  4 , then x = _______
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6. If m4  7 x  5 and m6  5x  13 , then m4 = _______ and m5 = _______
7. If m7  2x  7 and m10  6x  10 , then m7 = _______
8. If m4  9x  5 and m8  7 x  1 , then m8 = _______
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GEOMETRY Unit 4, Quadrilaterals
Notes 4-3, Squares and Rhombi
Squares and Rhombi
Name ________________________
Date __________ Period _________
Definition of a rhombus -
Rhombus Conjecture #1
(6-11):
The diagonals of a rhombus are ______________________.
Rhombus Conjecture #2
(6-13):
Each diagonal of a rhombus _______________________________.
Ex 1: Use rhombus ABCD to answer the following questions. (Treat each problem independently.)
(a) If AB = 7x + 3 and DC = 10x – 6, then AD = _______
(b) If AC = 32, then EC = _______
(c) If m1  2x  20 and m2  5x  4 , then x = ________
(d) If m7  5x  2 and m8  3x  10 , then m8 = _______
(e) If m5  51 , then mABC = _______ and mBCD = _______
(f) If m2  58  , then m3 = ________
Definition of a square -
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Ex 2: Use square ABCD to answer the following questions. (Treat each problem independently.)
(a) If AB = 2x + 3 and BC = 3x – 5, then DC = ________
(b) Find m8 _______
(c) If DB = 5x – 2 and EB = 2x + 4, then DB = _______ and AE = ________
Property
Parallelogram
Rectangle
Rhombus
Square
The diagonals bisect each
other.
The diagonals are
congruent.
Each diagonal bisects a
pair of opposite angles.
The diagonals are
perpendicular
Opposite angles are
congruent.
All four angles are right
angles.
All four sides are
congruent.
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GEOMETRY Unit 4, Quadrilaterals
Notes 4-4, Trapezoids and Kites
Name ________________________
Date __________ Period _________
Trapezoids and Kites
Definition of a trapezoid -
If the legs of a trapezoid are congruent, then
Isosceles Trapezoid Theorem #1
(6-14)
Isosceles Trapezoid Theorem #2
(6-15)
Use isosceles trapezoid ABCD above to answer the following questions:
Ex 1:
If mABC  116  , then mDAB = ______, mADC = ______, mDCB = ______
Ex 2: If AC = 8x – 1 and BD = 6x + 9, then AC = ______
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The median of a trapezoid is
Trapezoid Median Theorem
Use trapezoid ABCD below, where EF is a median, to answer the following questions:
Ex 3: AB = 6 and DC = 14, then EF = _______
Ex 4: If AB = 2x – 6, DC =3x – 3 and EF = 13, then x = ______
Ex 5: If mADC  43 , then mAEF = _______
Ex 6: If AE = 6, then AD = _______
Ex 7: If BF = 3x + 2 and FC = 5x – 4, then BF = ______ and BC = ______

A kite is a quadrilateral with two pairs of adjacent congruent sides.
Label the congruent sides on kite ABCD.
Ex 8: If AB = 3x + 1 and AD = 4x – 7, then AD = _______
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Use the “GG-Kites” applet on the website to come up with some conjectures about kites.
Kite Conjecture #1:__________________________________________________
Kite Conjecture #2:__________________________________________________
Kite Conjecture #3:____________________________________________
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