Warm-Up
BellExercises
Work
1. Solve 12 = x
10
60
2. The scale of a map is 1 cm : 10 mi. The actual
distance between two towns is 4.3 miles. Find the
length on the map.
3.
A model train engine is 9 centimeters long. The
actual engine is 18 meters long. What is the scale of
the model?
Warm-Up
Exercises
Notes
Definition
Similar Polygons
Two polygons are similar if corresponding angles are congruent
and corresponding side lengths are proportional.
EXAMPLE
Warm-Up1Exercises
Use similarity statements
In the diagram, ∆RST ~ ∆XYZ
a.
List all pairs of congruent
angles.
b. Check that the ratios of
corresponding side lengths are equal.
c.
Write the ratios of the corresponding side
lengths in a statement of proportionality.
Warm-Up
Exercises
Notes
Definition
Scale Factor
The ratio of the lengths of two corresponding sides of similar
polygons.
EXAMPLE
Warm-Up2Exercises
Find the scale factor
Determine whether the polygons are similar. If they
are, write a similarity statement and find the scale
factor of ZYXW to FGHJ.
EXAMPLE
Warm-Up3Exercises
Use similar polygons
ALGEBRA
In the diagram, ∆DEF ~ ∆MNP.
Find the value of x.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 2 and 3
In the diagram, ABCD ~ QRST.
2.
What is the scale factor of QRST to ABCD ?
3.
Find the value of x.
EXAMPLE
Warm-Up4Exercises
Find perimeters of similar figures
Swimming
A town is building a new
swimming pool. An
Olympic pool is
rectangular with length 50
meters and width 25
meters. The new pool will
be similar in shape, but
only 40 meters long.
a.
Find the scale factor of the new pool to an
Olympic pool.
b. Find the perimeter of an Olympic pool and the
new pool.
Warm-Up
Exercises
Notes
Theorem
Perimeters of Similar Polygons
If two polygons are similar, then the ratio of their perimeters is
equal to the ratios of their corresponding side lengths.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 4
In the diagram, ABCDE ~ FGHJK.
4. Find the scale factor of
FGHJK to ABCDE.
5.
Find the value of x.
6. Find The perimeter of ABCDE.
Warm-Up
Exercises
Notes
If two polygons are similar, then the ratio of any two
corresponding lengths in the polygons is equal to the scale
factor of the similar polygons.
(altitudes, medians, midsegments, etc.)
EXAMPLE
Warm-Up5Exercises
Use a scale factor
In the diagram, ∆TPR ~ ∆XPZ. Find the length of the
altitude PS .
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 5
7. In the diagram, ∆JKL ~ ∆ EFG. Find the length of
the median KM.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
1.
Are all congruent polygons similar polygons?
2.
Are all similar polygons congruent polygons?
Warm-Up
Exercises
For Tomorrow
Homework
HW: 6.1 Worksheet