Download ch 5 - Ani and Skye-2012

By: Andreani Lovett and
Skye Cole
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A parallelogram ( ) is a quadrilateral with
both pairs of opposite sides parallel.
Theorem 5-1(
OSC): Opposite sides of a
parallelogram are congruent.
Theorem 5-2(
OAC): Opposite angles of a
parallelogram are congruent
Theorem 5-3(
DB): Diagonals of a
parallelogram bisect each other.
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We know that WE
CR, so
angle COW is congruent to
angle EOW. Since the
diagonals of parallelograms
bisect each other CO is
congruent to OE. So Triangle
COW is congruent to Triangle
EOW.
Corresponding sides of
triangles are congruent so CW
is congruent to WE
According to 5-1 WE is
congruent to CR, and CW is
congruent to RE
By transitive property you can
prove that: RE
RC, CW
CE
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Theorem 5-4 (OSC ): If both pairs of opposite sides
of a quadrilateral are congruent, then the quadrilateral
is a parallelogram.
Theorem 5-5(One Pair CP ): If one pair of opposite
sides of a quadrilateral are both congruent and parallel,
then the quadrilateral is a parallelogram.
Theorem 5-6(OAC ): If both pairs of opposite angles
of a quadrilateral are congruent, then the quadrilateral
is a parallelogram.
Theorem 5-7(DB ): If the diagonals of a quadrilateral
bisect each other, then the quadrilateral is a
parallelogram.
Note: A parallelogram ( ) is a quadrilateral with both
pairs of opposite sides parallel.
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Its given that SA KC,
SK AC
SA and KC, SK and AC
are two pairs of
opposite sides.
According to the
definition of
parallelogram, a
parallelogram is a
quadrilateral with both
pairs of opposite sides
parallel.
So, the definition of a
parallelogram allows
us to reduce that
quadrilateral SACK is a
parallelogram.
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Theorem 5-8(//PE): If two lines are parallel,
then all points on one line are equidistant from
the other line.
Theorem 5-9(3//CST): If three parallel lines cut
off congruent segments on one transversal,
then they cut off congruent segments on every
transversal.
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Theorem 5-10(C. Mid-segment): A Line that
contains the midpoint of one side of a triangle
and is parallel to another side passes through
the midpoint of the third side
Theorem 5-11(Mid-segment): The segment that
joins the midpoints of two sides of a triangle
1: is parallel to the third side
2: is half as long as the third side.
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Given: L//M; A and B are any point on L;
Prove AC=BD
A
B
L
M
C
D
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Since AB and CD are contained in parallel
lines, AB//CD. Since AC and BD are coplanar
and are both perpendicular to M, they are
parallel. Thus ABDC is a parallelogram, by
definition of a parallelogram. Since opposite
sides AC and BD are congruent, AC=BD.
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A rectangle is a quadrilateral with four right
angles therefore, every rectangle is a
parallelogram.
A rhombus is a quadrilateral with four sides
therefore, every rhombus is a parallelogram.
A square is a quadrilateral with four right
angles and four congruent sides. It’s a
rhombus, square, and parallelogram together.
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5-12 (DRC)
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5-13 (DRH )
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The diagonals of a rectangle are congruent
The diagonals of a rhombus are perpendicular
5-14
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Each diagonal of a rhombus bisects two angles of the
rhombus
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5-15
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5-16
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The midpoint of the hypotenuse of a right triangle is
equidistant form the three vertices.
If an angle of a parallelogram is a right angle, then
the parallelogram is a rectangle
5-17
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If two consecutive sides of a parallelogram are
congruent, then the parallelogram is a rhombus
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Name each figure shown
A-parallelogram B- rectangle C- rhombus
D- square E-None of the above
1.
2.
3.
4.
5.
6.
MP is 6.5 then
AM is ?
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P
A
Not drawn to
scale.
M
K
<KAP is a right angle, and AM is a median.
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Trapezoid: a quadrilateral with exactly one pair
of parallel side
Isosceles trapezoid: a trapezoid with congruent
sides.
Theorem 15-8
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Base angles of an isosceles trapezoid are congruent.
15-9
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The median of a trapezoid is parallel to the bases
and has a length equal to the average of the base
lengths
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Looking good Ms. Sulkes
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From Ani
Thanks for learning with us today.
Goodbye.