Transcript Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)

Warm Up:
1.

Solve for x and y in the following parallelogram. What
properties of parallelograms did you use when solving?
B
C
o
(16x – 4)
5y – 1
2y + 8
(14x + 34)o
2.
3.
4.



A
D
What is the measure of CD?
What is the measure of Angle C?
What is the sum of the interior angles of a dodecagon?
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)

IF a quadrilateral is a parallelogram,
THEN its opposite sides are congruent.
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)


IF a quadrilateral is a parallelogram,
THEN its opposite sides are congruent.
IF both pairs of opposite sides of a
quadrilateral are congruent, THEN the
quadrilateral is a parallelogram.
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)

IF a quadrilateral is a parallelogram,
THEN its opposite angles are congruent.
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)


IF a quadrilateral is a parallelogram,
THEN its opposite angles are congruent.
IF both pairs of opposite angles of a
quadrilateral are congruent, THEN the
quadrilateral is a parallelogram.
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)

IF a quadrilateral is a parallelogram,
THEN its consecutive angles are
supplementary.
B
C
o
o
(180 – x)
A
xo
x
(180 – x)o
D
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)

IF a quadrilateral is a parallelogram,
THEN its consecutive angles are
supplementary.
B
C
o
o
(180 – x)
xo

x
(180 – x)o
A
D
IF an angle of a quadrilateral is
supplementary to both of its consecutive
angles, THEN the quadrilateral is a
parallelogram.
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)

IF a quadrilateral is a parallelogram,
THEN its diagonals bisect each other.
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)


IF a quadrilateral is a parallelogram,
THEN its diagonals bisect each other.
IF the diagonals of a quadrilateral
bisect each other, THEN the
quadrilateral is a parallelogram.
Conditions of Parallelograms (6.3) and
Special Parallelograms (6.4)

IF one pair of opposite sides of a
quadrilateral are parallel AND
congruent, THEN the quadrilateral is a
parallelogram.
Show that ABCD is a parallelogram for m = 12 and n = 9.5;
which one of the conditions of parallelograms did you use?
B
A
(2m + 31)o
(7m – 29)o
(12n + 11)o
D
C
Are each of the given quadrilaterals also
parallelograms? Justify your answer.
#1
#2
#3
7
7
Find x and y so the quadrilateral is a parallelogram.
(x – 12)o
B
A
(3y – 4)o
(4x – 8)o
D
(1/2 y)o
C
RECTANGLES
RECTANGLE



Four Right Angles
Congruent Diagonals
Properties of a Parallelogram
RHOMBUSES
RHOMBUS
Four Congruent Sides
 Perpendicular Diagonals
 Diagonals Bisect Opposite
Angles
 Properties of a Parallelogram

SQUARES
SQUARE


Properties of a Rectangle
Properties of a Rhombus
ABCD is a rhombus. Find the measure of Angle B.
(y + 2)o
B
C
(2y + 10)o
A
D
Show the diagonals
of square ABCD
are congruent
perpendicular
bisectors of each
other.
A (-1, 0)
B (-3, 5)
C (2, 7)
D (4, 2)