geometry: chapter 8 8.3: similar polygons. similar polygons two polygons are similar polygons if...
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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,
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.
ABC DEF
Ex. 1: In the diagram,
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.
ABC DEF
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 CongruenceNotice that any two congruent figures are also
similar. Their scale factor is 1:1. In triangle ABC and triangle DEF, the scale factor is
You can write
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 375.
51
5
and .ABC DEF ABC DEF
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, .
Find the length of the altitude .
MNP RST
NL
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 375.
Ex.5:
Answer: 21
In the diagram, .
Find the length of the altitude .
MNP RST
NL
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)