Transcript parallelogram - WordPress.com

Vocab. Check
How did you do?
1. Some
7. No
13. No
19. Some
2. No
8. Some
14. Some
20. All
3. Some
9. All
15. All
4. All
10. Some
16. All
5. No
11. Some
17. Some
6. Some
12. No
18. No
Unit Test Ch. 1-3
SOLUTIONS
1.
A
7.
C
13.
D
19.
A
2.
A
8.
D
14.
D
20.
C
3.
C
9.
C
15.
B
21.
B
4.
D
10.
B
16.
A
22.
A or D
5.
C
11.
A
17.
C
23.
C
6.
C
12.
B
18.
C
Review #6
1.
ABC has vertices A(0,0),
B(4,4) and C(8,0).
What is the equation of the
midsegment parallel to BC?
2. RED has vertices R(0,4), E(2,0), and D(6,4).
Graph and write the equation for the perpendicular
bisector of side RE. Then, find the circumcenter.
3. In ABC, centroid D is on median AM.
 AD = x + 6
 DM = 2x – 12

Find AM.
Page 290 8-16E, 36-42
8)parallelogram
 10) rectangle
 12) isosceles trapezoid
 14)kite
 16)rectangle








36. next slide
37. T
38. F
39 F
40. T
41. F
42. F
Parallelogram

A quadrilateral with both pairs of
opposite sides parallel.
Rhombus

A parallelogram with four congruent
sides.
Rectangle

A parallelogram with four right angles.
Square

A parallelogram with four congruent
sides and four right angles.
Kite

A quadrilateral with 2 pairs of adjacent
sides congruent and NO opposite sides
congruent.
Trapezoid

A quadrilateral with exactly one pair of
parallel sides.
Isosceles Trapezoid

A trapezoid whose nonparallel opposite
sides are CONGRUENT.
Properties of Parallelograms
Toolkit 6.2
Today’s Goal(s):
1.
To use relationships among sides and among
angles of parallelograms.
2.
To use relationships involving diagonals of
parallelograms or transversals.
If three (or more) parallel lines cut off congruent
segments on one transversal, then they cut off
congruent segments on every transversal.
5 Properties of a
Parallelogram…
1.
2.
3.
4.
5.
Opposite sides are congruent.
Opposite sides are also parallel.
Opposite angles are congruent.
The diagonals bisect each other.
Consecutive angles are supplementary.
ANGLES…
Opposite vs. Consecutive
CONGRUENT
SUPPLEMENTARY
EOC Review #6
Tuesday
1.
2.
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)
Point C is a centroid.
Solve for x.
Honors H.W. #28
pg. 297-300
#’s 2-34, 40-52 (evens)
Do you remember…?
5 Properties of a Parallelogram
Hint: 2-sides, 2-angles, 1-diagonals
Proving a shape is a
Parallelogram
Toolkit 6.3
Today’s Goal(s):
1. To use relationships among sides
and among angles to determine
whether a shape is a parallelogram.
There are 5 ways to PROVE that
a shape is a parallelogram:
1.
2.
3.
4.
5.
Show
Show
Show
Show
Show
that
that
that
that
that
BOTH pairs of opposite SIDES are parallel.
BOTH pairs of opposite sides are congruent.
BOTH pairs of opposite ANGLES are congruent.
the DIAGONALS bisect each other.
ONE PAIR of OPPOSITE sides is both congruent & parallel.
6.3 Examples
Determine whether the quadrilateral must be a
parallelogram. Explain.
6.3 Examples
#’s 10-15
#1
Find the value of x in each parallelogram.
1.
2.
x = 60
a = 18
#2
Find the measures of the numbered
angles for each parallelogram.
1.
2.
m1 = 38
m2 = 32
m3 = 110
m1 = 81
m2 = 28
m3 = 71
3.
m1 = 95
m2 = 37
m3 = 37
#3
Find the value of x for which ABCD must be a
parallelogram.
1.
2.
x=5
x=5
#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
#5
In a parallelogram one angle is 9 times the size
of another. Find the measures of the angles.
18 and 162
EOC Review #6
Wednesday
1.
ABC has a perimeter of 10x. 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?
Let’s set up some proofs! 
You try this one…
Ex.2: Two-Column Proof
Hmm… is there more than
one way to write this proof?
Statements
Reasons
Special Parallelograms
Toolkit #6.4
Today’s Goal(s):
1.
To use properties of diagonals
of rhombuses and rectangles.
Rhombus
A rhombus has ALL the properties of a
parallelogram, PLUS…
1.
2.
3.
All four sides of a rhombus are congruent.
Each diagonal of a rhombus BISECTS two angles.
The diagonals of a rhombus are perpendicular.
Rectangle
A rectangle has ALL the properties of a
parallelogram, PLUS…
1.
2.
All four angles of a rectangle are 90.
The diagonals of a rectangle are congruent.
AC  BD
Square

A square has ALL the properties of a
parallelogram, PLUS
ALL the properties of a rhombus, PLUS
ALL the properties of a rectangle.
So, that means that in a
square…
1.
2.
3.
4.
5.
All four sides are congruent.
All four angles are 90.
The diagonals BISECT each other.
The diagonals are perpendicular.
The diagonals are congruent.
Ex.1: Find the measures of the
numbered angles in each rhombus.
a.
b.
Ex.1:
You Try…
c.)
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
In-Class Practice
#1-3
#4-6
#7-9