Review & Trapezoids. Properties of a Parallelogram A BC D 1. Opposite sides are parallel. 2 Opposite...
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Transcript of Review & Trapezoids. Properties of a Parallelogram A BC D 1. Opposite sides are parallel. 2 Opposite...
Review & Trapezoids
Properties of a ParallelogramA
B C
D1. Opposite sides are parallel.
2 Opposite sides are congruent.
3. Opposite angles are congruent.
5. Diagonals bisect each other
4. Consecutive angles are supplementary
YES, we’re going to review again, & again, & again…
Properties of a Rhombus
A
B C
D
1. Opposite sides are parallel.
2 Opposite sides are congruent.
3. Opposite angles are congruent.
5. Diagonals bisect each other
4. Consecutive angles are supplementary
6. 4 congruent sides
7. Diagonals of a rhombus bisect the angles
8. Diagonals of a rhombus are perpendicular (bisectors)
Properties of a Rectangle1. Opposite sides are parallel.
2 Opposite sides are congruent.
3. Opposite angles are congruent.
5. Diagonals bisect each other
4. Consecutive angles are supplementary
6. 4 congruent sides
7. Diagonals of a rhombus bisect the angles
8. Diagonals of a rhombus are perpendicular (bisectors)
9. 4 right angles
10. Diagonals are congruent
Properties of a Square1. Opposite sides are parallel.2 Opposite sides are congruent.
3. Opposite angles are congruent.
5. Diagonals bisect each other
4. Consecutive angles are supplementary
6. 4 congruent sides
7. Diagonals of a rhombus bisect the angles
8. Diagonals of a rhombus are perpendicular (bisectors)
9. 4 right angles
10. Diagonals are congruentIt has it ALL!!!
Practice with squares
A B
CD
BX=
AX =
DB =
AC =
8.5
8.5
17
17
AB=
BC=
12
12
X12
DX = 8.5
mAXB= mXAB=90 45
And now…Properties of Trapezoids
Definition of a Trapezoid-
exactly one pair of parallel sides
OR
A quadrilateral with:
Definition of a Trapezoid- Parallel sides are called BASES
base
base
base
base
leg leg leg leg
Other nonparallel sides are called LEGS
Definition of an ISOSCELES Trapezoid-
A trapezoid with Congruent legs
base
base
leg leg
AND Congruent base angles
Name the following for trapezoid RSTW
R S
W T
THE BASES:
THE LEGS:
ONE PAIR OF BASE ANGLES
RS, TW
RW, STR & S ; or T & W
Median of a Trapezoid
AM
D
BN
C
6
1410
The median of any trapezoid is parallel to the bases
The median is equal to half the SUM of the base lengths
6 14
A median (MN) is a segment connecting the midpoints of the legs
MN = 10
6 14 2010
2 2
6 14
2
>
>
(sum of bases)
(half of sum)
Examples – find the length of the median
5
19
11-x
21+x
10 5
3 3
44
12
16
7.5
24?
2
11-x+21+x?
2
10 5
2
EF=
m1=
m2=
m3=
m4=
m5=
2
78
3
1304
5
115
9
A B
CD
E F
12
50
102
78
50
130
Isosceles trapezoid?
Corr s
Base s
Same Side interior - supplementary
Corr s
Same Side interior - supplementary
EF=
m1=
m2=
m3=
m4=
m5=
2
51
34
45
1
11
6
EF
JK
L M
16
51
129
51
129
51
Isosceles trapezoid?
