Transcript Warm up - Mrs. McAnelly's Online Math Resource

Let’s review the quadrilateral
properties we’ve learned so far:
All Quadrilaterals
Four angles
Four sides
Angles add to °360
Parallelograms
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are
supplementary
Diagonals bisect each other
Quadrilaterals – Day 3
Today we’re
going to learn
about special
parallelograms
Rectangle
Rhombus
Square
All Quadrilaterals
Parallelogram
Rectangle
 Is a parallelogram
 Has all the properties of
quadrilaterals above it in the flow
chart
PLUS has the following special properties:
 Angles are 90°
 Diagonals are congruent (contractor’s
theorem)
All Quadrilaterals
Parallelograms
Rectangles
Rhombi
Rhombus
 Is a parallelogram
 Has all the properties of
quadrilaterals above it
PLUS has the following
special properties:
 Sides are congruent
 Diagonals are perpendicular
 Diagonals are angle bisectors
All Quadrilaterals
Parallelogram
Rectangle
Rhombus
Square
SQUARE
Has all the properties of
quadrilaterals above it in the
flow chart.
SQUARE
Dad = Rectangle
Mom = Rhombus
 It gets the congruent sides mom
 It gets the angles from dad
 It gets the congruent diagonals from
dad
 It gets perpendicular diagonals from
mom
 It gets angle bisector diagonals from
mom
All Quadrilaterals
Parallelogram
Rectangle
Rhombus
Square
Whew….
I never
realized there
was so much
to learn about
quadrilaterals!
Let’s practice…
Find the measures of
all the sides,
diagonals and angles.
FRED is a
rectangle
R
F
M
14 in.
D
20°
26 in.
mDM = 15 in.
E
CRIS is a rhombus
Find all angle, side
and diagonal
measures
R
I
28°
8 ft
17 ft
15 ft
C
S
True or False
1. Every square is a rhombus
2. Every rhombus is a square
3. Every rectangle is a square
4. Every square is a rectangle
5. All rhombi are
parallelograms
6. Every parallelogram is a
rectangle.
Quadrilaterals
Day 4
Kite
Trapezoid
Trapezium
This is what the flow
chart will look like at
the end of this class.
Convex
Quadrilaterals
Parallelograms
Rectangles
Square
Rhombi
Trapezoid
Right
Trapezoid
Isosceles
Trapezoid
Trapezium
Kite
Properties of a trapezoid
♥ A trapezoid has one and only one pair of
parallel sides.
♥ Two pair of consecutive, supplementary
angles.
Midsegment of a trapezoid
♥ As the name suggests, a midsegment of a
trapezoid is a segment in the middle of a
trapezoid.
♥ It is parallel with the parallel sides.
♥ Behold
Properties of a trapezoid
♥ Which is the midsegment?
♥ Which is not?
Properties of a trapezoid
♥ The length of the midsegment is the average
of the lengths of the parallel sides.
♥ The midsegment is equidistant from each
parallel side.
Length 1
Length 1 + Length 2
2
Length 2
Properties of a trapezoid
♥ Let’s practice
10
x
20
2x - 4 + 3x + 2 = 2x + 4
2
5x - 2 = 2x + 4
2
5x - 2 = 4x + 8
X = 10
= 15
2x - 4
2x + 4
16
24
CHECK
Does 16 + 32 = 24?
3x + 2
32
2
If yes, have a personal celebration!!
If no, then find your mistake or start over.
Try this
X
A
BY = 7
Find ?
CZ = 12
Y
?
C
AM = 2
M
X+5
B
Find the lengths of the
parallel segments
when x = 2
Z
? = X + 10
Check to make sure these
numbers work…
2 + 12 = 7
2
YEA!!
Try this…
If AZ = 31 and
CX = 25, find BY
BY = 28
C
B
A
X
Y
Z
Properties of a TRAPEZIUM:
A quadrilateral with NO parallel sides.
A special Trapezium is a KITE
♥ 2 pair of consecutive congruent
sides
♥ Opposite sides are NOT
congruent
♥ Only ONE pair of opposite angles are
congruent.
♥ Diagonals are perpendicular
♥ Only ONE diagonal
is bisected
White boards…
Your Assignment
6-6 Worksheet