# LESSON 6.2 PROPERTIES OF PARALLELOGRAMS

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```					               LESSON 6.2
PROPERTIES OF PARALLELOGRAMS

OBJECTIVE:
Use relationships among sides and
among angles of parallelograms

Use relationships involving diagonals
or parallelograms and transversals
Slide Courtesy of Miss Fisher
1                   Modified 1/28/08
Definitions
Check for Understanding: Starting with Ð K move
counterclockwise around   JKLM to name pairs of
consecutive angles.

Consecutive angles of a polygon
share a common side.
____________________

In   JKLM, ÐJ and ÐM are consecutive
angles, as are ÐJ and Ð___. ÐJ and Ð___
K      L
opposite Courtesy angles.
are ____________ of Miss Fisher
Slide
2                      Modified 1/28/08
Theorems
Check for Understanding: If RT and US bisect one
another at point M, name two pairs of @ segments.

Theorem 6.1
___________ sides of a parallelogram are @.
Opposite

Theorem 6.2
@
Opposite angles of a parallelogram are ____.

Theorem 6.3
bisect
The diagonals of a parallelogram _________
each other.
Slide Courtesy of Miss Fisher
3                        Modified 1/28/08
Theorems Con’t

Theorem 6.4

If three (or more) parallel lines cut off
congruent segments on one transversal,
then _____________________________
they cut off congruent segments
_________________________________
on every transversal.

BD @ DF
_________

Slide Courtesy of Miss Fisher
4                     Modified 1/28/08
EXAMPLE #1
Find the value of x in       ABCD.
Then find mÐA.

Opposite angles of a                     mÐB = x + 15
parallelogram are congruent
_________                    = 60 + 15
= 75°
so, x + 15 = 135 - x
2x + 15 = 135                   *mÐA + mÐB = 180
2x = 120                     mÐA + 75 = 180
x = 60                           mÐA = 105°
*Recall, consecutive angles in a parallelogram are
Slide Courtesy of Miss Fisher
5    supplementary, since __________________________.
// lines à same-side int. Ðs supp.
Modified 1/28/08
EXAMPLE #2

Find the values of x
and y in    KLMN.

bisect
Diagonals of a parallelogram ______ each other,
so Substitute 7y -16 for x in the second equation.
x = 7y – 16              and             2x + 5 = 5y
x = 7(3) – 16                    2(7y – 16) + 5 = 5y
x = 21 – 16                         14y – 32 + 5 = 5y
x=5                                         14y – 27 = 5y
-27 = -9y
Substitute 3 for y in the first                     3=y
Slide Courtesy of Miss Fisher
6     equation.             Modified 1/28/08
EXAMPLE #3
In the figure DH || CG || BF || AE,
Find EH.

If three (or more) parallel lines cut off congruent
segments on one transversal, then
_________________________________
they cut off congruent segments on every
_________________________________
transversal, so EF = FG = GH.

EH = EF + FG + GH
EH = 2.5 + 2.5 + 2.5
EH = 7.5 units
Slide Courtesy of Miss Fisher
7                         Modified 1/28/08
Assignment: pg 297 #2-16, even,
17, 19, 22, 34-35, 39-41

Slide Courtesy of Miss Fisher
8                  Modified 1/28/08

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