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Slide 1
Slide 2
Review In ABC, centroid D is on median AM. AD = x + 6 DM = 2x
12 Find AM. Did you draw a picture? Did you think about the key
word?
Slide 3
Parallelogram A quadrilateral with both pairs of opposite sides
parallel.
Slide 4
Parallelograms have Properties Click to view
Slide 5
Properties of Parallelograms Toolkit 6.2 Todays Goal(s): 1. To
use relationships among sides and among angles of parallelograms.
2. To use relationships involving diagonals of parallelograms or
transversals.
Slide 6
Properties of Every Parallelogram: Both pairs of opposite sides
are congruent. Both pairs of opposite angles are congruent.
Consecutive adjacent angles are supplementary. Diagonals bisect
each other.
Slide 7
ANGLES Opposite vs. Consecutive CONGRUENT SUPPLEMENTARY
Slide 8
5 Properties of a Parallelogram 1.Opposite sides are congruent.
2.Opposite sides are also parallel. 3.Opposite angles are
congruent. 4.The diagonals bisect each other. 5.Consecutive angles
are supplementary. Mark the diagrams!
Slide 9
6.3 Examples Determine whether the quadrilateral must be a
parallelogram. Explain.
Slide 10
#1 Find the value of x in each parallelogram. 1.2. x = 60a =
18
Slide 11
#2 Find the measures of the numbered angles for each
parallelogram. 1.2.3. m 1 = 38 m 1 = 81 m 1 = 95 m 2 = 32 m 2 = 28
m 2 = 37 m 3 = 110 m 3 = 71 m 3 = 37
Slide 12
#3 Find the value of x for which ABCD must be a parallelogram.
1.2. x = 5
Slide 13
#4 Use the given information to find the lengths of all four
sides of ABCD. The perimeter is 66 cm. AD is 5 cm less than three
times AB. x = 9.5 BC = AD = 23.5 AB = CD = 9.5
Slide 14
#5 In a parallelogram one angle is 9 times the size of another.
Find the measures of the angles. 18 and 162
Slide 15
Slide 16
Special Parallelograms Rectangle Rhombus Square
Slide 17
Rectangle A parallelogram with four right angles.
Slide 18
What are the properties of a rectangle? All the properties of
every parallelogram. (What are these properties?) All four angles
are right angles. The diagonals are congruent.
Slide 19
Rectangle A rectangle has ALL the properties of a
parallelogram, PLUS 1.All four angles of a rectangle are 90 . 2.The
diagonals of a rectangle are congruent. AC BD
Slide 20
Ex.2: Find the length of the diagonals of rectangle ABCD. a.)AC
= 2y + 4 and BD = 6y 5 b.)AC = 5y 9 and BD = y + 5
Slide 21
Rhombus A parallelogram with four congruent sides.
Slide 22
What are the properties of a rhombus? All the properties of
every parallelogram. The diagonals are perpendicular. Each diagonal
bisects two angles of the rhombus.
Slide 23
Rhombus A rhombus has ALL the properties of a parallelogram,
PLUS 1.All four sides of a rhombus are congruent. 2.Each diagonal
of a rhombus BISECTS two angles. 3.The diagonals of a rhombus are
perpendicular.
Slide 24
Ex.1: Find the measures of the numbered angles in each rhombus.
a.b.
Slide 25
Square A parallelogram with four congruent sides and four right
angles.
Slide 26
A square has ALL the properties of a parallelogram, PLUS ALL
the properties of a rhombus, PLUS ALL the properties of a
rectangle. A square is a parallelogram, a rectangle, and a rhombus!
Square
Slide 27
So, that means that in a square 1.All four sides are congruent.
2.All four angles are 90 . 3.The diagonals BISECT each other. 4.The
diagonals are perpendicular. 5.The diagonals are congruent.
Slide 28
Summary Slide What is a parallelogram? Properties of Every
Parallelogram: What is a rectangle? What are the properties of a
rectangle? What is a rhombus? What are the properties of a rhombus?
What is a square? What are the properties of a square?
Slide 29
Your turn: 1. Do: On your paper, list the properties of a
square. 2. Think: How can you use these properties to determine the
measures of sides, angles, and diagonals of a parallelogram? Be
ready to share your thoughts! Home
Slide 30
Kite A quadrilateral with 2 pairs of adjacent sides congruent
and NO opposite sides congruent.
Slide 31
Trapezoid A quadrilateral with exactly one pair of parallel
sides.
Slide 32
Isosceles Trapezoid A trapezoid whose nonparallel opposite
sides are CONGRUENT.
Slide 33
Slide 34
If three (or more) parallel lines cut off congruent segments on
one transversal, then they cut off congruent segments on every
transversal.
Slide 35
Do you remember? 5 Properties of a Parallelogram Hint: 2-sides,
2-angles, 1-diagonals
Slide 36
Proving a shape is a Parallelogram Toolkit 6.3 Todays Goal(s):
1.To use relationships among sides and among angles to determine
whether a shape is a parallelogram.
Slide 37
There are 5 ways to PROVE that a shape is a parallelogram:
1.Show that BOTH pairs of opposite SIDES are parallel. 2.Show that
BOTH pairs of opposite sides are congruent. 3.Show that BOTH pairs
of opposite ANGLES are congruent. 4.Show that the DIAGONALS bisect
each other. 5.Show that ONE PAIR of OPPOSITE sides is both
congruent & parallel.
Slide 38
Lets set up some proofs!
Slide 39
You try this one
Slide 40
Ex.2: Two-Column Proof
Slide 41
Hmm is there more than one way to write this proof?
StatementsReasons
Slide 42
Special Parallelograms Toolkit #6.4 Todays Goal(s): 1. To use
properties of diagonals of rhombuses and rectangles.
Slide 43
EOC Review #6 Wednesday 1. ABC has a perimeter of 10 x. The
midpoints of the triangle are joined together to form another
triangle. What is the difference in the perimeters of the two
triangles? 2. Where is the center of the largest circle that you
could draw INSIDE a given triangle?
Slide 44
EOC Review #6 Tuesday 1.Plot the following points on a graph
and decide if AD is an altitude, median, angle bisector or
perpendicular bisector. A(6,7) B(8,2) C(2,2) D(6,2) 2.Point C is a
centroid. Solve for x.