Section 5.5 Properties of Quadrilaterals
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Transcript 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
AD BC
AB II DC
AD II BC
DAB BCD
ADC ABC
DAB suppl. ABC
BCD suppl. ADC
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
AD AB
Prove: ABCD is a rectangle
Statements
Reasons
1. ABCD is a
parallelogram
1. Given
2. AD AB
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
m<ADC = 120
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
AD = 2n-53
Find:
a.) AD
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. BC AD
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,
AD = 19
m<ACD = 144
(In an isosceles trapezoid,
upper base angles are
congruent)
Rhoad, Richard, George Milauskas, and Robert
Whippie. Geometry for Enjoyment and
Challenge. New Edition. Evanston, Illinois:
McDougall, Littell & Company, 1997. 241-248.
Print.