Transcript Geometry 8_3 Similar Polygons

GEOMETRY: Chapter 8
8.3: Similar Polygons
Similar Polygons
Two polygons are similar polygons if
corresponding angles are congruent and
corresponding side lengths are proportional.
Ex. 1: In the diagram,
ABC
DEF
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.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 373.
Ex. 1: In the diagram,
ABC
DEF
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.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 373.
Scale Factor
If two polygons are similar, then the ratio of the
lengths of two corresponding sides is called
the scale factor.
Ex. 2: Determine whether the polygons are
similar. If they are, write a similarity
statement and find the scale factor of
RSTU to DEFG.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 373.
Ex. 2: Determine whether the polygons are
similar. If they are, write a similarity
statement and find the scale factor of
RSTU to DEFG.
Answer:RSTU ~ DEFG; the scale factor is
3:2
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 373.
Ex. 3: In the diagram, triangle ABC ~
triangle GHJ.
Find the value of x.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 374.
Ex. 3: In the diagram, triangle ABC ~
triangle GHJ.
Find the value of x.
Answer: 24
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 374.
Theorem 8.1: 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.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 374.
Ex. 4: You are constructing a rectangular
play area. A play ground is rectangular
with side lengths 25 meters and width
15 meters. The new play area will be
similar in shape, but only 10 meters in
length.
a. Find the scale factor of the new play
area to the playground.
b. Find the perimeter of the playground
and the play area.
Ex. 4: You are constructing a rectangular
play area. A play ground is rectangular
with side lengths 25 meters and width
15 meters. The new play area will be
similar in shape, but only 10 meters in
length.
a. Find the scale factor of the new play
area to the playground.
b. Find the perimeter of the playground
and the play area.
answer: a. 2:5; b. 80m and 32 m
Similarity and Congruence
Notice that any two congruent figures are also
similar. Their scale factor is 1:1. In triangle
ABC and triangle DEF, the scale factor is
5
1
5
You can write ABC
DEF and ABC  DEF .
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 375.
Corresponding Lengths in Similar Polygons
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.
Ex.5: In the diagram,
MNP
RST .
Find the length of the altitude NL.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 375.
Ex.5: In the diagram,
MNP
RST .
Find the length of the altitude NL.
Answer: 21
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 375.
8.3, p. 475, #2-18 evens, 19-29 odds, 39-42 all
(19 questions)