Lesson 6-2 Properties of Parallelograms

					              Lesson 6-2 Properties of Parallelograms

Warm-Up

Find the sum of the measures of the interior angles of a convex
hexagon.




Definition of a Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides.
To write the name of a parallelogram, you use the symbol          .




Properties of the Parallelogram




                                                                       Another Property:

                                                                       Each diagonal of the
                                                                       parallelogram
                                                                       divides the
                                                                       parallelogram into
                                                                       two congruent
                                                                       triangles.
Model Problems
1) In parallelogram ABCD, AB = x + 20 and CD = 6x – 50. Find the value of x.




2) If EFGH is a parallelogram,

a) Find FJ.




b) Find EG.




3) The measures of two consecutive angles of a parallelogram are in the ratio 3:7.
Find the measure of an acute angle of the parallelogram.




Exercise
1) In the figure at right, WXYZ is a parallelogram.

a) Find ZY.
2) Find      .




3) In the accompanying diagram of ADCE, ADCB is a parallelogram.
If BC = CE, and m<BEC = 65°, find m <A and m <D.




Finding the Missing Vertex of a Parallelogram

Model Problem

Three vertices of   JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of
vertex M.
Exercise
Three vertices of    PQRS are P(–3, –2), Q(–1, 4), and S(5, 0). Find the coordinates of
vertex R.




Lesson Summary
1) By definition, a parallelogram is _________________________________________

__________________________________________________________________.

2) List five properties of the parallelogram:

1)


2)


3)


4)


5)
HOMEWORK

				
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posted:8/30/2012
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