Chapter 8: Quadrilaterals
Sections 1 - 4
Name _____________________________
Geometry Notes
Quadrilaterals
A __________________ is a plane figure whose sides are ______________ or more coplanar
segments that ________________________ only at their ______________________ (the
vertices). Consecutive sides cannot be _______________________, and no more than
_____ sides can meet at any one _______________.
Review the quadrilaterals …
1. A ______________________________ is a
quadrilateral with two pairs of parallel sides.
Number by definition
2. A ______________________________ is a
quadrilateral with four right angles.
3. A ______________________________ is a
quadrilateral with four congruent sides.
4. A ___________________ is a quadrilateral with four
right angles and four congruent sides.
5. A __________________________ is a quadrilateral
with exactly one pair of parallel sides.
We name quadrilaterals, in fact all __________________,
as we did triangles: by the vertices in order.
 Name this quadrilateral:
___________________
The _______________________ of a polygon is a
_____________ segment with endpoints that are any two
____________________________ vertices of the polygon.
 Identify the diagonals:
___________________
Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Degrees in Polygons
The sum of the interior angles in a polygon increases by _________ degrees with each
Theorem 8.1
side we add. Why is this? _____________________________________________________.
Polygon Interior Angles Theorem
The sum of the measures of the interior angles (_____) of a convex
polygon with _______ sides is given by:
S = ( ____ – ____ ) 180˚
What about the exterior angles?
An __________________ angle of a polygon is created by simply _____________________ the
Theorem 8.2
sides of the polygon to create the exterior _____________________.
Polygon Exterior Angles Theorem
The sum of the measures of the exterior angles of a convex
polygon, ______ angle at each _______________, is
360˚
Why?
This “shrinking” heptagon – similar to the aperture of a camera or the iris in your eye –
illustrates the sum of the exterior angles.

What is the sum when the aperture is closed? ___________________.
Page 2 of 13
Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Let’s try a few:
Sides
Example
Name
Sum of Interior Angles
Sum of Exterior Angles
3
4
5
6
7
8
9
10
Ready? Action!
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Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Practice 8.1
Page 511: 11 – 16 all, 18
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Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Page 511 - 12: 19, 20, 21, 32
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Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Parallelograms
We’ve spent some time defining ________________________ and we can use these
definitions to _________________ them. But, in order to do that, we have to
______________ some things about them – prove that they ____________ the definition.
Explore ............................... handouts, straws, ruler, scissors, protractor, thumbtack, foamboard
1. You’ll need three straws—two that are the same length and one of a different length.
 Mark their midpoints.
2. How to make the drawings:
a. Take two straws and cross them so that they bisect
each other, fastening them with a thumbtack
through their midpoints.
b. Place the drawing paper on top of the foamboard and affix the straws on the
paper by pushing the tack through the paper, in to the board.
c. Mark dots at the endpoints, and use a straightedge to connect these points.
 Make your figures large enough so you can easily measure the angles.
d. Keep each drawing and label it by shape.
3. Follow the directions on each handout to find the different quadrilaterals that
result from each combination of lengths and angles of the diagonals (straws).
 Complete the chart below to summarize your results.
If the diagonals of a quadrilateral are …
1
not perpendicular and not congruent
2
not perpendicular but are congruent
3
perpendicular but are not congruent
4
congruent and perpendicular
Then the quadrilateral is a …
Do we all agree on the types of _________________________ we created?! GOOD.
Page 6 of 13
Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Now, let’s take your four drawings and use them for the next activity.
1. Draw in the diagonals of each quadrilateral you created with the straws.
2. Use a ruler to measure the lengths of the sides and diagonals in each quadrilateral.
3. Use a protractor to measure all of the angles in the quadrilateral, including those
formed by the intersection of the diagonals.
4. Complete the chart based on your drawings and measurements. Indicate with an
X
the quadrilaterals that have each property.
Property
Parallelogram Rectangle
Rhombus
Square
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
Diagonals are perpendicular.
Diagonals are congruent.
All sides are congruent.
All angles are right angles.
Using your observations and chart, complete the statements
theorems (You proved this, right?)
about the diagonals of special parallelograms:
1. A parallelogram is a rhombus if and only if its diagonals are _______________________.
2. A parallelogram is a rectangle if and only if its diagonals are ______________________.
3. A parallelogram is a square if and only if its diagonals are both ____________________
and ________________________.
Page 7 of 13
Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Well done! … But, not finished! … And, keep your drawings!
Look at your drawings and at the chart. What one general statement can we make
about all four figures?
They are all _____________________________.
Why?
Because opposite sides of each figure are ___________________________. This is, after
all the definition of a _____________________________, isn’t it?

The fact that the ____________________ sides of a parallelogram are
___________________ gives parallelograms even more special properties.
Let’s get on with the SPECIALNESS …
Isolate some of the critical attributes from your chart. Copy your “X”s here.
Property
Parallelogram Rectangle
Rhombus
Square
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
What do you notice?
Page 8 of 13
Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
How can we use this to prove anything?
State a property that justifies each conclusion.
JKL  LMJ ; JKL
is ___________________
LMJ
Why? ________________________________________________________
JKLM is a parallelogram
JM
is parallel to
KL
because _______________________________________________________
MN  NK , because ________________________________________________________________
Complete each statement and justify your conclusion.
If EF = 14, HG = ___________
Why? ________________________________________________________
If
m HEF=75 o , m FGH=______, and m EHG=______
Why? ________________________________________________________
EFGH is a parallelogram
If EG = 25, EI = ________, because _____________________________________________________
If HI = 10, HF = ________, because ____________________________________________________
If
m EFG=112 o , m FGH=______ , because ________________________________________
Page 9 of 13
Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Try a few more …
 Find the values of x and y for each quadrilateral.
 Justify your answers.
Think – Diagonals of a rectangle:
1. are ______________________
2. ______________________ each other.
X = ___________
Y = __________
Think – Diagonals of a square:
1. are ______________________
2. are ______________________
3. ______________________ eachother.
X = ___________
Y = __________
I think you’ve got the hang of this. So, let’s practice.
Yeah, it looks like a lot, but we just covered three sections of the chapter…
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Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Practice 8.2 – 8.4
Page 518 - 19: 3 – 8, 13 - 15
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Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Page 526 - 27: 8 – 10, 19 - 20
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Chapter 8: Quadrilaterals ....................................................................................... Sections 1 - 4
Page 538: 26 – 29
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