Musical Math

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Transcript Musical Math

Materials
Reminders
Get out your agenda if you see
your name below. I would like
to have you in my FLEX
Wednesday.
Period 2
Period 7
Use the Pythagorean Theorem to
determine whether or not the following
triangle is a right triangle.
3
1
2
4-7 Similar Polygons
How do I identify similar polygons
and find the missing measures of
similar polygons?
Important
Vocabulary
Polygon – three or more attached line segments in
a plane that for a closed figure
Similar Polygons (symbol A~B) – polygons with
the same exact shape but possibly differing in size
(think enlargements or reductions)
Corresponding Parts (A ↔ B) – parts of two or
more similar figures that match
Important
Vocabulary
Congruent – parts of two figures that have the
same measure
Scale Factor – what you would multiply the
corresponding sides of one similar figure by to
get a second similar figure
Questions:
How do I
identify similar
polygons?
Notes:
Steps
1. Find the ratios between all of the corresponding sides
of the two figures
2. Determine (using division) whether or not all of the
ratios are equal
3. If the ratios are equal, the polygons are similar
Example:
2
5
3
7.5
2
= 0. 6
3
5
= 0. 6
7.5
Beause the ratios of the corresponding sides
are equal, the figures are similar.
Concept Check
1. Get into groups of 2 and get one WHITE
BOARD and a DE marker
2. Determine whether the following two figures
are similar.
10
5
4
8
7
15
3. Be prepared to share with the class.
Questions:
How do I
determine the
scale factor
between two
similar figures?
Notes:
Steps
1. Divide a measure on the NEW figure by the
corresponding measure on the OLD figure.
2. The result is the SCALE FACTOR.
Example:
1
A
3
B
The scale factor from triangle A (OLD) to triangle
B (NEW) is:
𝑁𝐸𝑊 3
= =3
𝑂𝐿𝐷
1
Concept Check
1. Get into groups of 2 and get one WHITE
BOARD and a DE marker
2. Find the listed scale factors for the following
similar figures.
1. From trapezoid A to trapezoid B
2. From trapezoid B to trapezoid A
4
A
12
B
3. Be prepared to share with the class.
Questions:
How do I use
proportions to
find missing
measures?
Notes:
Steps
1. Set up a proportion using two corresponding sides
with known measures and two corresponding sides
with one unknown measure (the missing measure)
2. Find the cross products
3. Solve for the variable
Example:
5
2
A
3
2 3
=
5 𝑥
B
2𝑥 = 15
𝑥 = 7.5
x
This is also the scale factor
from A to B
Concept Check
1. Get into groups of 2 and get one WHITE
BOARD and a DE marker
2. Use the concept of PROPORTIONS to find the
missing measure, x, on the following similar
figures.
0.7
2.1
x
2.2
3. Be prepared to share with the class.
Homework
Page 222-223; 1-12 and
18-19
AND Cornell Notes
Summary