Upload
beverley-cooper
View
213
Download
0
Tags:
Embed Size (px)
Citation preview
1
Geometry Section 7-1A Geometry Section 7-1A
Changing the Size of Changing the Size of FiguresFigures
Page 462Page 462You will need a calculator You will need a calculator
with sin/cos/tan in 2 with sin/cos/tan in 2 weeks.weeks.
Freshmen - TI 30 XII S Freshmen - TI 30 XII S recommended. Around $15. You’ll recommended. Around $15. You’ll
need it for Alg. II.need it for Alg. II.
3
Similar Figures:Similar Figures:Similar Figures- Figures that have the same shape, but not necessarily the same size. Think enlargements or reductions.
These figures are similar. Same shape, but not the same size.
These are not similar. None of these have the same shape.
Pg.462
4
Similar Figures:Similar Figures:Scale Factor: the amount of enlargement or reduction needed to get one figure from another.
If the scale factor is greater than 1, the similar figure is an enlargement; if the scale factor is less than 1, it is a reduction.
Pg.462
5
Explore:Explore:Enlarge the side lengths by a factor of 3.
Pg.463
Choose a side in the original figure. Identify the corresponding side in your enlarged version. What is the ratio between the 2 sides? Is it the
same for other sets of corresponding sides?
Use your protractor to measure the corresponding sets of angles.
What is their ratio?
31
11
6
Explore:Explore:Enlarge the side lengths by a factor of 3.
Pg.463
Choose a side in the original figure. Identify the corresponding side in your enlarged version. What is the ratio between the 2 sides? Is it the
same for other sets of corresponding sides?
Use your protractor to measure the corresponding sets of angles.
What is their ratio?
31
11
The ratio of the lengths of two corresponding sides of similar figures is the similarity ratio.
7
Example:Example:ABC is similar to XYZ.
Pg.463
AB 5XY 9
Find the similarity ratio of ABC to XYZ.
=
Find the similarity ratio of XYZ to ABC .
XY 9AB 5
=
z
8
Try It:Try It:a. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the
figure on the left to the figure on the right.
Pg.464
If similar, find the similarity ratio of the figure on the right to the figure on the left.
Similar
2/1
1/2
9
Try It:Try It:b. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the
figure on the left to the figure on the right.
Pg.464
If similar, find the similarity ratio of the figure on the right to the figure on the left.
Similar
1/3
3/1
10
Try It:Try It:c. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the
figure on the left to the figure on the right.
Pg.464
Not similar
11
Try It:Try It:d. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the
figure on the left to the figure on the right.
Pg.464
If similar, find the similarity ratio of the figure on the right to the figure on the left.
Similar;1/3
3/1
12
Definition:Definition:
Definition of similar: Two polygons are similar if and only if:
1)Their corresponding angles are congruent and2)Their corresponding side lengths are proportional.
Pg.464
13
Reflect:Reflect:Suppose you enlarge or reduce a figure to make a similar figure.
Pg.465
What happens to the measure of each of the angles?
The angle measures stay the same.
What happens to the length of each line segment?
Side lengths are multiplied by the scale factor.
If Figure X is similar to Figure Y, how is the similarity ratio from X to Y related to the similarity ratio from Y to X?
They are reciprocals of each other.
14
Exercises:Exercises:
#4
Pg.465
If you reduce a 15cm x 20cm rectangle by using a scale factor of 3/5, what will the dimensions of
the reduced rectangle be?
35
15 x = 9
35
20 x = 12
9cm x 12cm
15
Exercises:Exercises:
#5
Pg.465
If you enlarge a 9 in x 12 in rectangle by using a scale factor of 2.5, what will the new dimensions be?
9 x 2.5 = 22.5
12 x 2.5 = 30
22.5 in x 30 in
16
Exercises:Exercises:
#6, 7
Pg.466
True or False?
Any 2 squares are similar.
True
Any 2 rectangles are similar.
False. The ratio of the lengths could be different from the ratio of the widths.
17
Exercises:Exercises:
#8, 9
Pg.466
True or False?
Any 2 rhombuses are similar.
False. The sides remain in proportion, but the angles can be changed.
Any 2 equilateral triangles are similar.
True. All angles will be 60o and all sides will be proportional.
18
Exercises:Exercises:
#12
Pg.466
A to B = 1/3
Each pair of figures is similar, and the length of corresponding sides are shown. Find the similarity
ratio of Figure A to B and of B to A.
B to A = 3/1
19
Exercises:Exercises:
#14
Pg.466
Not similar.
State whether or not each pair of figures is similar. If similar, find the similarity ratio of the figure on the left to the figure on the right. If not similar,
explain why.
Sets of corresponding sides do not
have the same ratio.
20
Exercises:Exercises:
#15
Pg.466
23
State whether or not each pair of figures is similar. If similar, find the similarity ratio of the figure on the left to the figure on the right. If not similar,
explain why.
Similar