Transcript 7-2: Similar Polygons

7-2: Similar Polygons
Rigor: Define and apply properties of similar polygons
Relevance: Indirect measurement and scale drawings!
Similar figures – have the same shape, but
not necessarily the same size
- Symbol is ~
Extended Proportions and Scale Factors
Extended Proportion - 3 or more equivalent ratios
are set equal to each other
used when comparing corresponding sides of
similar polygons
The scale factor of the corresponding sides can
be found by simplifying any of the ratios in the
proportion.
𝐴𝐵
𝐵𝐶
𝐴𝐶
EX:
=
=
𝑋𝑌
𝑌𝑍
𝑋𝑍
15
20
25
= =
6
8
10
SF =
5
2
EX 1: Understanding Similar Figures
DEFG ~ HIJK
What are the pairs of congruent angles?
What is the extended proportion for the
corresponding side lengths?
EX 2: Determining Similarity
Are the polygons similar? If so, write a similarity
statement and determine the scale factor.
a)
b)
c)
EX 3: ABCD ~ EFGD. Solve for x and y
EX 4: Real World Application
Step 1: Determine whether the height or width will fill
the space first.
Step 2: Use the scale factor from step 1 to calculate
the other dimension. Convert back to feet.
Notes: Scale Drawings
Scale Drawings – all drawing lengths are
proportional to corresponding actual
lengths
Ratios (Scales) of scale drawings can have
different units!
Example = 1cm : 200m
Example: Scale Drawings
The Seattle Space Needle is 605ft tall.
Tommy decides to make a scale drawing
on an 8.5in by 11in piece of paper. If
Tommy chooses a 1in : 50ft scale, is his
paper big enough?
7-2 Homework
Heading: 7-2 pg 469
Problems: #12, 13, 16, 17, 19, 20, 30, 35
Due Thursday, February 12th.