Transcript parallelogram

Section 6.2 – Properties of
Parallelograms
Students will be able to:
•Use relationships among sides and angles of
parallelograms
•Use relationships among diagonals of
parallelograms
Lesson Vocabulary:
•Parallelogram
•Opposite Angles
•Opposite Sides
•Consecutive Angles
A parallelogram is a quadrilateral with both pairs
of opposite sides parallel.
Essential Understanding:
Parallelograms have special properties regarding
their sides, angles, and diagonals.
In a quadrilateral, opposite sides do not share a
vertex and opposite angles do not share a side.
Practice Problem 1:
Find the value(s) of the variable(s) in each
parallelogram.
Angles of a polygon that share a side are
consecutive angles.
A Parallelogram has opposite sides that are
parallel and its consecutive angels are same side
interior angles.
Problem 1b:
Find the value of x in each parallelogram.
Problem 1:
What is <P in Parallelogram PQRS?
Reminder: Solving Systems of Equations:
Using Substitution:
Solve one equation for a variable
Using Elimination:
Multiply (if necessary) to get 1
variable
Substitute that value in the second
equation for the given variable.
Solve for one variable
Sub that value into either equation to
equation to get
get value of other variable.
to be opposites
Add or Subtract Equations from
each other
Solve for one variable
Sub that value into either
value of other variable.
Problem 1:
Solve a system of linear equations to find the values of x
and y in Parallelogram KLMN. What are KM and LN?
Problem 2:
Solve a system of linear equations to find the values of x
and y in Parallelogram PQRS. What are PR and SQ?
Extra Problems:
Find the measures of the numbered angles for
each parallelogram.