Transcript Slide 1

SECTION 8-2, 8-4, 8-5
spi.3.2.H
Jim Smith JCHS
Parallelograms are quadrilaterals with
Both pairs of opposite sides parallel.
ABCD
A
B
›
D
›
C
5 Things About Parallelograms
Definition
1) Both Pairs Opp Sides Parallel
Properties
2)
3)
4)
5)
Both Pairs Opp Sides Congruent
Both Pairs Opp Angles Congruent
Consecutive Angles Supplementary
Diagonals Bisect Each Other
Both Pairs Opp Sides Parallel
A
AB||DC
1 and 6
3 and 8
2
7
D
8
1
3
4
6
5
B
AD||BC
2 and 5
4 and 7
C
Alternate Int Angles Are Congruent
Both Pairs Opp Sides Congruent
23
42
X
X = 23
2Y – 16 = 42
2Y - 16
2Y = 58
Y = 29
Both Pairs Opposite Angles
Congruent
5Y - 5
65°
X
115°
X = 65
5Y – 5 = 115
5Y = 120
Y = 24
Consecutive Angles
Are Supplementary
1
2
3
4
Supplementary angles have a sum of 180
Diagonals Bisect Each Other
BX = XD
AX = XC
A
B
C
X
D
Rectangles Are Parallelograms
With 4 Right Angles
All 5 Things About Parallelograms
Are True…PLUS
1) All angles = 90°
2) Diagonals are congruent
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
Congruent Pairs of Angles
1
2
3
9
11
4
10
12
8
7
6
5
Congruent Pairs of Angles
1
2
3
9
11
4
10
12
8
7
6
5
A Rhombus Is A Parallelogram With
4 Congruent Sides
All 5 Things About Parallelograms Are
True…PLUS
1) 4 congruent sides
2) Diagonal are perpendicular
3) Diagonals bisect opposite angles
4 congruent sides
10
3Y + 1 = 10
3Y = 9
Y=3
3Y + 1
Diagonal are perpendicular
A
B
3
4
X
D
C
AB = 5
The perimeter Of
rhombus ABCD =
20
XC = 3
DB = 8
The Square Is The Most
Special Of All !!
Everything That’s True For
All The Others Is True For
Squares.
QUADRILATERALS
PARALLELOGRAMS
RECTANGLES
RHOMBI
SQUARES