Transcript 6-2 Properties of Parallelograms

Properties of Parallelograms
LESSON 6-2
Additional Examples
Use
KMOQ to find m O.
Q and O are consecutive angles of
KMOQ, so they are supplementary.
m O + m Q = 180
m O + 35 = 180
m O = 145
Definition of supplementary angles
Substitute 35 for m Q.
Subtract 35 from each side.
Quick Check
HELP
GEOMETRY
Properties of Parallelograms
LESSON 6-2
Additional Examples
Quick Check
Find the value of x in
x + 15 = 135 – x
2x + 15 = 135
2x = 120
x = 60
m B = 60 + 15 = 75
m A + m B = 180
m A + 75 = 180
m A = 105
HELP
ABCD. Then find m A.
Opposite angles of a
are congruent.
Add x to each side.
Subtract 15 from each side.
Divide each side by 2.
Substitute 60 for x.
Consecutive angles of a
parallelogram are supplementary.
Substitute 75 for m B.
Subtract 75 from each side.
GEOMETRY
Properties of Parallelograms
LESSON 6-2
Additional Examples
Find the values of x and y in
x = 7y – 16
2x + 5 = 5y
2(7y – 16) + 5 = 5y
14y – 32 + 5 = 5y
14y – 27 = 5y
–27 = –9y
The diagonals of a parallelogram
bisect each other.
Substitute 7y – 16 for x in the
second equation to solve for y.
Distribute.
Simplify.
Subtract 14y from each side.
3=y
Divide each side by –9.
x = 7(3) – 16
Substitute 3 for y in the first
equation to solve for x.
x=5
So x = 5 and y = 3.
HELP
KLMN.
Simplify.
Quick Check
GEOMETRY
Properties of Parallelograms
LESSON 6-2
Additional Examples
Theorem 6-4 states If three (or more) parallel lines cut off
congruent segments on one transversal, then they cut off congruent
segments on every transversal. Explain how to divide a blank card into
five equal rows using Theorem 6-4 and a sheet of lined paper.
Place a corner of the top of the card on the first line of the lined paper.
Place any other corner on the sixth line.
Mark the points where the lines intersect one side of the card.
Mark the points where the lines intersect the opposite side of the card.
Connect the marks on opposite sides using a straightedge.
If you use the same-side bottom corner, the lines are parallel to the top of
the card. If you use the opposite corner, the lines are parallel to the
diagonal of the card.
Quick Check
HELP
GEOMETRY