Geometry
Quadrilaterals Day 2 Warm Up
Name_________________________
1. Find the value of x.
98
120
82
x
Find the sum of the measures of the interior angles for each convex polygon.
2. nonagon
3. 17-gon
4. Find the coordinates of the midpoint of segment AB with endpoints A(–2, 6) and B(10, 4).
5. Find the distance between (–2, 6) and (10, 4).
Parallelograms
Today we will understand parallelograms
And at the end of today, you will be able to determine lengths of diagonals, angles and sides
in a parallelogram
parallelogram –
If a quadrilateral is a parallelogram, then:
- its opposite sides are congruent.
- its opposite angles are congruent.
- its consecutive angles are supplementary.
- its diagonals bisect each other.
Examples:
1. Find the values of x and y.
x+ 4
y
65
12
2. Find the indicated measure given the JKLM is a parallelogram.
a. NM
b. KM
c. m  JML
d. m  KML
K
L
2
N
110
30
J
3. Find the values of a and b in the parallelogram.
M
a - 12
(b + 10)
36
30
4. Find the indicated measures in parallelogram ABCD.
B
C
a. m  BCD
100
b. If BE = 9, find BD.
E
37
A
D
How do I know if a quadrilateral is a parallelogram?
If….
- both pairs of opposite sides of a quadrilateral are congruent
- both pairs of opposite angles of a quadrilateral are congruent
- one pair of opposite sides of a quadrilateral are congruent and parallel
- the diagonals of a quadrilateral bisect each other
Examples:
1. In quadrilateral WXYZ, m  W = 42°, m  X = 138°, m  Y = 42°. Find m  Z. Is WXYZ a
parallelogram?
C
2. For what value of x is quadrilateral CDEF a parallelogram?
5x - 8
F
3x
D
E
What reasoning can you use to show that the quadrilateral is a parallelogram?
3.
4.
5.
7 in
30 m
65
5 in
115
5 in
7 in
30 m
115
65