### Section 5.5 Properties of Quadrilaterals

```Both pairs of opposite sides are parallel
 Both pairs of opposite sides are
congruent
 The opposite angles are congruent
 The diagonals bisect each other
 Any pair of consecutive angles are
supplementary

AB  DC
AB II DC
 DAB   BCD
 DAB suppl.  ABC
AE  EC
DE  EB
Has all properties of a parallelogram
 All angles are right angles
 Diagonals are congruent

Two disjoint pairs of consecutive sides are
congruent
 The diagonals are perpendicular
 One diagonal is the perpendicular
bisector of the other
 One of the diagonals bisects a pair of
opposite angles
 One pair of opposite angles are
congruent

Has all properties of a parallelogram and
of a kite (half properties become full
properties
 All sides are congruent
 The diagonals bisect the angles
 The diagonals are perpendicular
bisectors of each other
 The diagonals divide the rhombus into
four congruent right triangles

Has all properties of a rectangle and a
rhombus
 The diagonals form four isosceles right
triangles

The legs are congruent
 The bases are parallel
 The lower base angles are congruent
 The upper base angles are congruent
 The diagonals are congruent
 Any lower base angle is supplementary
to any upper base angle

Given:
ABCD is a rectangle
DA = 5x
CB = 25
DC = 2x
Find:
a.) The value of x
b.) The perimeter of ABCD
a.) 5x = 25
x=5
b.) DA= 25
CB = 25
DC = 10
AB = 10
Perimeter = 25 + 25 + 10 + 10
Perimeter = 70
Given: ABCD is a parallelogram
Prove: ABCD is a rectangle
Statements
Reasons
1. ABCD is a
parallelogram
1. Given
3. <DAB is a right
<
2. Given
4. ABCD is a
rectangle
4. If a
parallelogram
contains at least
one right <, it is a
rectangle
3. Perpendicular
lines form right <s
Given:
ABCD is a parallelogram
<DAB = n
<ABC = 2n
Find: m <BCD and m < ADC
2n+n=180
3n=180
n=60
2n=120
m <BCD = 60
Given:
ABCD is a rhombus
AB = 2x-5
BC = x
a.) Find the value of x
b.) Find the perimeter
Given: ABCD is a
parallelogram
Prove: ▲AED ▲BEC
Given:
m<CAB = n
m<CDB = 4n
Find:
b.) m<ACD
2x-5 = x
X=5
AB = 2x-5
AB = 5
Perimeter = 5 + 5 + 5 + 5
Perimeter = 20
Statements
Reasons
1. ABCD is a parallelogram
1. Given
2. In a parallelogram, opp. Sides
are congruent
3. AC Bisects BD
3. In a parallelogram, diagonals
bisect each other
4. BE  ED
4. If a ray bisects a segment, it
divides the segment into 2
congruent segments
5. BD Bisects AC
5. Same as 3
6. AE  EC
7. ▲AED  ▲BEC
6. Same as 4
7. SSS (2,4,6)
n + 4n = 180
5n = 180
n = 36
4n = 144
2n-53 = 19
Therefore,