Parallelograms Rectangles Rhombi Squares. HOMEWORK: 5.5/16, 911,16, 17 5.6/113, 28. Parallelograms. DEFINITION. Parallelograms are quadrilaterals with Both pairs of opposite sides parallel. ABCD. ›. A. B. ›. ›. ›. ›. ›. D. C. 4 Properties of Parallelograms. Definition
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Parallelograms Rectangles
Rhombi Squares
HOMEWORK:
5.5/16, 911,16, 17
5.6/113, 28
Parallelograms
DEFINITION
Parallelograms are quadrilaterals with
Both pairs of opposite sides parallel.
ABCD
›
A
B
›
›
›
›
›
D
C
4 Properties of Parallelograms
Definition
Quadrilateral with both pairs opposite sides parallel
Properties
1) Both Pairs Opp Sides Congruent
2) Both Pairs Opp Angles Congruent
3) Consecutive Angles Supplementary
4) Diagonals Bisect Each Other
Both Pairs Opp Sides Parallel
Add a transversal and ..
A
B
ABDC
1 and 6
3 and 8
ADBC
2 and 5
4 and 7
1
3
2
4
7
5
8
6
D
C
Alternate Int Angles Are Congruent
Both Pairs Opp Sides Congruent
X = 23
2Y – 16 = 42
2Y = 58
Y = 29
23
42
2Y  16
X
X = 65
5Y – 5 = 115
5Y = 120
Y = 24
5Y  5
X
115°
65°
Consecutive Angles
Are Supplementary
1
3
2
4
Supplementary angles have a sum of 180
Consecutive Angles
Are Supplementary
145˚
x
x = 180  145
x = 35˚
Diagonals Bisect Each Other
B
C
BX = XD


X
AX = XC


A
D
Diagonals Bisect Each Other
B
C
25
2x5
A
D
RECTANGLES
Definition
Rectangles Are Parallelograms With 4 Right Angles
All 4 properties About Parallelograms Are True…
PLUS
All Angles = 90°
If 1 Angle In A Parallelogram Is A Right
Angle, Then All 4 Angles Are Right Angles
This gives us
right triangles also




Diagonals Are Congruent
This Gives Us 4 Congruent Segments
And 4 Isosceles Triangles
This Tells Us A Lot About The Angles
Diagonals Are Congruent
3x2
3x2 = 25
25
3x= 27
x = 9
Congruent Pairs of Angles
2
3
4
1
11
9
10
12
8
5
7
6
Congruent Pairs of Angles
2
3
4
1
11
9
10
12
8
5
7
6
Congruent Pairs of Angles
Find the angle measures
37˚
p
b
a
m
k
s
f
r
h
d
t
RHOMBI
Definition
A Rhombus Is A Parallelogram With
4 Congruent Sides
All 4 properties About Parallelograms Are True…
PLUS
4 congruent sides
10
3Y + 1 = 10
3Y = 9
Y = 3
3Y + 1
Diagonal are perpendicular
A
B
Remember the Pythagorean thm.
5
AB =
The perimeter Of
rhombus ABCD =
XC =
DB =
3
4
X
20
D
C
3
8
Diagonals bisect opposite angles
A
B
z
y
y = 50˚
X
z= 30˚
40˚
50˚
D
C
SQUARE
The Square Is The Most Special Of All !!
Everything That’s True For
All The Others Is True For Squares.
Regular Quadrilateral
SQUARE
Regular Parallelogram
Definitions
Equiangular Rhombus
Equilateral Rectangle
Equiangular
Equilateral
Diagonals ≅ & ┴
diagonals bisect each other
diagonals bisect opposite <‘s
Opposite <‘s ≅
Opposite sides ≅
Consecutive <‘s = 180˚
Has all the properties of the parallelogram, rectangle and rhombus
QUADRILATERALS
PARALLELOGRAMS
RECTANGLES
RHOMBI
SQUARES
Quadrilaterals
4 sides, angles add to 360
Parallelograms
Opp sides parallel, Opp sides congruent, Opp angles congruent,
Consecutive angles =180, Diagonals bisect
Rhombus
All sides are congruent.
Diagonals are perpendicular.
Opp angles are bisected.
Rectangle
All angles are congruent.
Diagonals are congruent.
Square
Everything