Download 5_6 parallelograms

Homework 5.3, Exercise 6
11
=2a + 1
By the Triangle Inequality theorem,
the sum of any two sides of a triangle
is greater than the third side.
(a) + (2a + 1) > 𝟑𝟒
3a + 1 >34
3a > 𝟑𝟑
a> 𝟏𝟏
5.5: Properties of Parallelograms
5.5: Properties of Parallelograms
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Parallelogram opposite angles theorem:
The opposite angles of a parallelogram
are congruent.
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Parallelogram consecutive angles theorem:
The consecutive angles angles of a
parallelogram are supplementary ( their
sum add up to 180°.
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Parallelogram opposite sides theorem:
The opposite sides of a parallelogram are
congruent.
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Parallelogram Diagonals theorem:
The diagonals of a parallelogram bisect
each other.
34 cm
27 cm
132°
48°
16 in
14 cm
63 m
80
63°
78°
(11 x + 3) + (13 x + 9) = 180
X= 7
100°
x-1=2x -8
X= 7
6
14 x-1= 7+12x
X= 4
55
5.6: Properties of specialParallelograms
Investigation:
Double-Edged Straightedge Theorem:
If two parallel lines are intercepted by a second pair
of parallel lines that are the same distance apart as
the first pair, then the parallelogram formed is a
Rhombus.
Rhombus: Equilateral parallelogram
The diagonals of a rhombus are
perpendicular,
and they
bisect each other.
What do the diagonals of a rhombus do to its angles?
The diagonals of a rhombus
bisect
the angles of the rhombus.
Rectangle:
Equiangular parallelogram
Compare the lengths of the two diagonals of a rectangle.
Rectangle Diagonals Theorem:
The diagonals of a rectangle
are congruent and bisect each other.
Square:
Equilateral rectangle.
Equiangular rhombus.
Regular quadrilateral.
Square Diagonals Theorem:
The diagonals of a square are
congruent, perpendicular, and bisect each other.
Summary
20
37°
45°
90°
Homework:
Workbook 5.5: 1-9,
except 8.
Workbook 5.6: 1-13