Download 6.2: Properties of Parallelograms

Bell work: Identify all congruent
triangles from the picture below
6.2: Properties of
Parallelograms
If Statements
(AKA Conditional Statements)
Recall…
Theorem 6.2: The sum of the
measures of the exterior angles of
any polygon is 360
If and Only If statements
(AKA Biconditional statements)
A
triangle has three equal sides if
and only if it has three equal
angles
Notes
A
parallelogram is a quadrilateral (4 sided
shape) where the opposite sides are all
parallel
 In
a quadrilateral, opposite angles are
angles that share no side, and opposite
sides are sides that share no vertex
 For
any polygon, consecutive angles are
angles that are next to each other; ones
that share a common side
 Theorem
6-3/6-8: A quadrilateral is a
parallelogram…if and only if its opposite sides
are congruent
 Theorem 6-4/6-9: A quadrilateral is a
parallelogram…if and only if its consecutive
angles are supplementary
 Theorem 6-5/6-10: A quadrilateral is a
parallelogram…if and only if its opposite
angles are congruent
 Theorem 6-6/6-11: A quadrilateral is a
parallelogram…if and only if its diagonals
bisect each other
What
is the
measure of
angle P?
If
we adjust
the lamp such
that angle
s=86, what
would angle R
be?
Proofs of theorem 6-3 and 6-5
Suppose I construct the diagonals
of a parallelogram…

In other words…if we have parallel lines where
they are all crossed by the same line, and
segments of that line are congruent, then any
line that crosses the parallel ones will form
segments of the same size
6.3: Proving a
quadrilateral is a
parallelogram
Find a value for y that makes the
shape a parallelogram
For what values of x and y must the
shape below be a parallelogram?
Homework:
 Section
6.2, page 364: 9, 13, 14, 15,
17, 21, 23, 27
Honors:
 Section
Add 28, 30, 38
6.3, page 372: 7-9, 13
Honors:
Add 16, 22, 23
Find the value of
each variable or
side
 Section
6.3
13. Can you prove this is a
parallelogram using the
given information?