Download Geometry B Date: ______ 6.2 Properties of Parallelograms

Geometry B
Date: _____________
6.2 Properties of Parallelograms
Objective: Apply and use properties of parallelograms to solve problems
Recall:

Quadrilaterals are polygons with ___________ sides and ____________ angles.

The sum of their interior angles is _____________

Some quadrilaterals have special properties and are given their own name.
Parallelogram

Definition: ________________________________________________________________

Properties:
o Opposite sides are _____________________ and _____________________
o Opposite angles are __________________________
o Same-side (consecutive interior) angles are ____________________________
o Diagonals in a parallelogram _________________ one another.

This means when diagonals cross, they _______________________________
Naming Parallelograms:
_____________________
or
_____________________
Ex. 1: Using Properties of Parallelograms
In
CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°.
a. Find CF
b. Find mEFC
c. Find DF
Ex. 2: Using Properties of Parallelograms to Find Measures
WXYZ is a parallelogram.
a. Find YZ
b. Find mZ
Practice:
EFGH is a parallelogram.
a. Find JG.
b. Find FH
Ex. 3: Quadrilaterals in the Coordinate Plane
Three vertices of
JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of vertex M.
(Since JKLM is a parallelogram, both pairs of opposite sides must be parallel.)
Step 1: Graph the given points.
L
____
Step 2: Find the slope of KL by
counting the units from K to L.
K
Step 3: Start at J and count the
same number of units.
Step 4: Count the slope to verify
_____
_____
that LM || KJ
J
Practice: Three vertices of
vertex R.
PQRS are P(–3, –2), Q(–1, 4), and S(5, 0). Find the coordinates of
Q
S
P
HW: 6.2 Worksheet