Download Scale factor, r, is the ratio of any length in a scale drawing relative to

CC Geometry R
Aim #2: How do we create scale drawings?
Do Now: Below is a picture of a bicycle. Which of the images below it appears to be a
well-scaled image of the bicycle? Why?
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(1) (2) (3) Scale factor, r, is the ratio of any length in a scale drawing relative to its
corresponding length in the original figure.
• If r > 1, this results in an _____________________ of the original figure
• If 0 < r < 1, this results in a ____________________ of the original figure.
Example 1:
Use construction tools to create a scale drawing of ΔABC with a
scale factor r = 2 with center A.
C
A
B
Example 2:
Use construction tools to create a scale drawing of ΔABC with a
scale factor r = 2 with center C.
C
A
B
The triangles created by the two examples are ________________.
Both triangles apply the same criteria: Two pairs of sides that are equal and a pair
of included angles that are equal; ________.
a) Using your ruler, measure the length of BC and B'C' in mm. What do you notice?
b) Using our protractor, measure angles B, C, B', and C'. What do you notice?
Properties of a well-scaled drawing:
1) Corresponding ____________ are equal in measure.
2) Corresponding ____________ are all in the same proportion.
The ____________ _______________ is the term for theconstant of
proportionality by which all lengths are scaled.
If you created a scale drawing of triangle ABC again, but oriented it at a different
angle, would the drawing still be a scale drawing? Why or why not?
1) Create a scale drawing of ΔDEF with a scale factor of r = 3 with center D.
What properties does your scale drawing share with the pre-image?
D
F
E
1
2) Create a scale drawing ofΔXYZ with a scale factor of r = /2 with center Z.
You will need your compass to locate the midpoint of two sides.
Which construction will you need to do?
__________________
Y
X
2.
Z
1
3) Create a scale drawing ofΔPQR with a scale factor of r = /4 with center Q.
P
R
Q
4) ΔABC is below and one side of scale drawingΔA'B'C'. Complete the scale drawing
by copying angles A and C. Use your ruler (in mm) to determine the scale factor: ____
A'
A
B
C
C'
5) ΔEFG is below and one angle of scale drawingΔE'F'G'. Complete the scale drawing
so that the scale factor of r = 3. What properties do the scale drawing and
pre-image share?
E
G
F
Angle measures are congruent
G'
Sides are in proportion
Let's sum it up!
• There are two key properties of a scale drawing of a figure: corresponding
angles are equal and corresponding lengths are in proportion.
• The properties of scale drawings have to do with lengths and relative angles, not
location or orientation.
• Provided a triangle and a scale factor, or a triangle and one piece of the scale
drawing of the triangle, it is possible to create a complete scale drawing of the
triangle using a compass and straightedge. No matter which method is used to
create the scale drawing, we rely on triangle congruence criteria to ensure that a
unique triangle is determined.