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, QuadrilateralsName ______

Notes 4-1, ParallelogramsDate ______Period ______

Parallelograms(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

yourconjecture 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 xEx 6: Solve for x and y

find .find and .

Draw a picture to illustrate

your conjecture Parallelogram Conjecture#3 (6-3):

Consecutive angles of a parallelogram are ______.

Ex 7: If , find , and .Ex 8: Solve for x and find .

Ex 9: Find and .

Parallelogram Conjecture#4 (6-4):

The diagonals of a parallelogram ______

Ex 10: If AE = 8, find EC.

Ex 11: IfEB = 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.

GEOMETRY Unit 4, Quadrilaterals

Name ______

Notes 4-2, RectanglesDate ______Period ______

Rectangles

  • 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:

PropertyWhy 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 = ______
  1. If EC = 12x – 4 and DE = 44, then x = ______
  1. If AE = 5x – 2 and DB = 6x + 16, then AC = ______
  1. If , then= ______and= ______

Use rectangle ABCD to answer the following questions:

  1. If and, then x = ______
  2. If and, then= ______and = ______
  1. If and, then = ______
  1. If and, then = ______

GEOMETRY Unit 4, QuadrilateralsName ______

Notes 4-3, Squares and RhombiDate ______Period ______

Squares and Rhombi

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 and, then x = ______

(d)If and, then = ______

(e)If , then = ______and = ______

(f)If , then = ______

Definition of a square -

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 ______

(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 areperpendicular
Opposite angles are congruent.
All four angles are right angles.
All four sides are congruent.

GEOMETRY Unit 4, QuadrilateralsName ______

Notes 4-4, Trapezoids and KitesDate ______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)

Useisosceles trapezoid ABCD above to answer the following questions:

Ex 1:If , then = ______, = ______, = ______

Ex 2:If AC = 8x – 1 and BD = 6x + 9, then AC = ______

The median of a trapezoid is

Trapezoid Median Theorem

Use trapezoid ABCDbelow, where EF is a median, to answer the following questions:

Ex 3:AB = 6 and DC = 14, thenEF = ______

Ex 4:If AB = 2x – 6, DC=3x – 3 and EF = 13, then x = ______

Ex 5:If , then = ______

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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