Chapter 3
Geometry and Measurement
What You Will Learn:
 To identify, describe, and draw:
 Parallel line segments
 Perpendicular line segments
 To draw:
 Perpendicular bisectors
 Angle bisectors
 Generalize rules for finding the area of:
 Parallelograms
 Triangles
 Explain how the area of a rectangle can be used to find
the area of:
 Parallelograms
 Triangles
3.1 – Parallel and Perpendicular Line
Segments
What you will learn:
To identify, describe, and draw:
Parallel line segments
Perpendicular line segments
Parallel
 Describes lines in the same plane that never
cross, or intersect
 The perpendicular distance btw parallel line
segments must be the same at each end of the
line segments.
 They are always marked using “arrows”
 http://www.mathopenref.com/parallel.html
Some ways to create parallel line
segments:
Using paper folding
Using a ruler and a right triangle
Example:
 Draw a line segment, AB. Draw another line
segment, CD, parallel to AB.
Example:
 Draw a line segment, AB. Draw another line segment,
CD, parallel to AB.
B
D
B
C
A
Use a ruler to
draw a line
segment.
A
Slide the triangle, draw a parallel line.
D
B
C
A
Label the endpoints (A, B, C, D).
Mark the lines with arrows to show the lines are parallel.
Perpendicular
 Describes lines that intersect at right angles
(90°)
 They are marked using a small square
right angle
 http://www.mathopenref.com/perpendicular.html
Some ways to create perpendicular line
segments:
Using paper folding (p. 85)
Using a ruler and protractor (p. 85)
 http://www.mathopenref.com/constperplinepoint.html
Assignment
P. 86
#1, 3-5, 7, 9, 11, Math Link
Still Good? #2, 8, 10, 12, 13
ProStar? #14-16
right angle
3.2 – Draw Perpendicular Bisectors
Bisect:
Bi means “two.” Sect means “cut.” So, Bisect
means to cut in two.
Perpendicular bisector
A line that divides a line segment in half and is
at right angles (90°) to the line segment.
Equal line segments are marked with “hash”
marks
Some ways to create a perpendicular
bisector:
Using a compass (p. 90)
http://www.mathopenref.com/constbisectline.html
Using a ruler and a right triangle (p. 91)
Using paper folding (p. 91)
Assignment
P. 92, # 1-5, 8
Still Good? # 6, 7, 9, MathLink
ProStar? #10
3.3 – Draw Angle Bisectors
Terms:
 Acute angle
Less than 90°
An angle that is less than 90°
 Obtuse angle
An angle that is more than 90°
Greater than 90°
 Angle Bisector
A line that divides an angle into two equal parts
Equal angles are marked with the same symbol
Some ways to create an angle bisector
include:
Using a ruler and compass (p. 95)
http://www.mathopenref.com/constbisectangle.html
Using a ruler and protractor (p. 95)
Using paper folding (p.95)
Assignment
P. 97, # 1 & 2, 5, 6, 8
Still Good? # 3 & 4, 9, 11, 13, MathLink
ProStar? #12, 14, 15
Less than 90°: acute
Greater than 90°: obtuse
Angle Bisector
3.4 – Area of a Parallelogram
Area of a rectangle: Area = length x width
6 cm
w
A=lxw
4 cm
A = 6 cm x 4 cm
2
l
A = 24 cm
Parallelogram
A four-sided figure with opposite sides parallel
and equal in length
 http://www.mathopenref.com/parallelogramarea.html
Making a Parallelogram from a Rectangle
cut
paste
 Base
A side of a two-dimensional closed figure
Common symbol is b
 Height
The perpendicular distance from the base to the
opposite side
Common symbol is h
h
b
 Suggest a formula for calculating the area of a
parallelogram.
Area of a Rectangle vs.
Area of a Parallelogram
8 cm
8 cm
12 cm
12 cm
Are they the same? Try it!
Area = length x width
= 12 cm x 8 cm
= 96 cm2
h
b
Area = base x height
= 12 cm x 8 cm
= 96 cm2
Sometimes it is
necessary to extend the
line of the base to
measure the height
Key Ideas
The formula for the area of a rectangle can
be used to determine the formula for the
area of a parallelogram.
The formula for the area of a
parallelogram is A = b x h, where b is the
base and h is the height.
The height of a parallelogram is ALWAYS
perpendicular to its base.
h
b
Assignment
P. 104, # 1-3, 5, 7, 9, 11
Still Good? # 13-18, MathLink
ProStar? # 19, 20
h
b
A=bxh
3.5 – Area of a Triangle
What you will learn:
Develop the formula for the area of a triangle
Calculate the area of a triangle
What we know:
The area of a rectangle
A = l x w
The area of a parallelogram
A = b x h
Key Ideas
Cut the rectangle in half
h
h
b
A=bxh
b
A=bxh
2
Cut the area in half
 The formula for the area of a rectangle or parallelogram can be used
to determine the formula for the area of a triangle
 The formula for the area of a triangle is A = b x h 2, or A = b x h,
2
where b is the base of the triangle and h is the height of the triangle.
 The height of the triangle is always measured perpendicular to its
base.
 http://www.mathopenref.com/trianglearea.html
Your Assignment
P. 113, #1-3 as a class.
Area of a Triangle, Notebook
Area of a Triangle Questions, Notebook
P. 113, #4a), 5b)
No problem? #8, 10, 11
Still good? #13-15
Pro Star? #16-19