Download 6.4: Rectangles and Squares

Geometry
6.4: Rectangles and Squares
Name _____________________________
A rectangle is
A square is
How are rectangles, squares, quadrilaterals, parallelograms, and rhombuses related?
Because rectangles and squares are parallelograms…..
1. The opposite sides are _________________________
2. The opposite angles are ________________________
3. The consecutive angles are _____________________
4. The diagonals ____________________ each other
Example 1: Find the measure of the angle of length of the side.
a. ABCD is a rectangle
b. RSTU is a square
AD = _____ AB = _______
UT = _____
m ∠A = ____ m ∠B = _____
m ∠R = ______
m ∠S = _______
m ∠C = _____
m ∠T = ______
m ∠U = ______
m ∠D = ______
RU = ______ RS = _______
Diagonal Properties of a Rectangle and a Square
The diagonals of a rectangle
1.
2.
The diagonals of a square:
1.
2.
3.
Example 2: Find the missing angles measures or side lengths
Example 2: Find the missing angle measures or side lengths of the RECTANGLES.
a.
b.
XM = ______
KM = ______
XL = ______
m ∠1 = _____
m ∠2 = ______ m ∠3 = ______
NL = ______
m ∠1 = ____
m ∠2 = ______
m ∠6 = _____
m ∠4 = ______ m ∠5 = _______
m ∠7 = _____
m ∠8 = ______ m ∠9 = _______
m ∠3 = ______
Example 3: Find the missing angle measures or side lengths of the SQUARES.
RS = _____
RU = ______
SX = ______
m ∠1 = _____
m ∠2 = _____
RX =_____
XT = _____
RT= _______
m ∠4 = _____
m ∠5 =______ m ∠6= _______
US = _____
m ∠3 = ______
6.6: Reasoning about Quadrilaterals
Rectangle:
Square:
Definition:
Definition:
Draw a diagram:
Draw a diagram:
Properties:
Because it’s a parallelogram…
1.
2.
3.
4.
Properties:
Because it’s a parallelogram…
1.
2.
3.
4.
Special properties of rectangles…
5.
Special properties of squares…
5.
6.
6.
7.
Example 4: Are you given enough information to conclude that the figure is a square?
a)
b)
Example 5: If the diagonals of a quadrilateral bisect each other, then the quadrilateral
must be a ___________________.
A. Rectangle
B. rhombus
C. square
D. parallelogram
HW: 6.4/6.6 Worksheet #2