Scale Factor Of A Polygon
24-hour interval 3/Lesson iii: Similar Polygons
Goals:
1. Identify similar polygons
2. Use similar polygons to solve problems.
Opener: Explore the Polygons in GSP
Click here: Similar Polygons
Introduction:
Recall that two shapes are congruent if they have the aforementioned shape and size. When 2 shapes have the same shape but different sizes, we call the shapes similar. You can also think of like objects or shapes equally scaled versions of each other.
Instance: Toys cars and airplanes that are scaled down versions of the real objects. In this section we will merely concentrate on similar polygons.
Recall that a polygon is a closed shape consisting of a finite number of line segments that do not cross each other. Below are a few examples of polygons:
Definitions:
one. Polygons whose corresponding angles are congruent and whose corresponding sides are proportional are called similar polygons .
Example:
Check the angles and respective sides:
All the angles in a rectangle are coinciding to each other and now cheque that the sides are proportional to each other.
2. Scale gene : If two polygons are like, then the ratio of the lengths of the 2 corresponding sides is the scale factor.
The scale factor=k in the to a higher place example is determined the following way:
2*k=4, so grand=2.
Now nosotros volition accept the same relationship between the other two sides:
ii*k=3, so thousand=ii.
Solving Problems with Similar Polygons:
There are three ways to solve for a missing side length of a polygon when you are given a pair of similar polygons.
1. "Scale Factor" Method: Given that two polygons are similar, there is a scale factor between the corresponding sides of the polygons, call the calibration factor, g. Nosotros can use the human relationship betwixt two of the corresponding sides, to notice the rest of the corresponding sides.
Click hither to measure the side IK.
2. "Relative Size" Method: Now we will utilize the relationship between the sides of one polygon to notice the lengths of the sides of the other polygons.
3. Set a proportion to detect the missing side length. We know that a proportion is two ratios that are equal to each other, so you can use either ratio, the relative size or the scale factor, and detect the missing side.
Applications Using Similar Polygons:
1. A large flag flown in front of a school is 4ft. tall by 8ft. and 5in. broad. Suppose you want to make a scaled down version of the flag. If you lot want the flag to be 2ft. tall, how broad should the scaled downwardly version of the flag exist? Utilize any of the three methods we have simply discussed.
Hint: Make sure that all of your units are the aforementioned in the ratios that yous set up.
Theorem:
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
Explore these similar polygons in GSP see if the theorem holds:
Return to EMAT6690 Primary Page
Render to Geometry Lesson Plan Principal
Scale Factor Of A Polygon,
Source: http://jwilson.coe.uga.edu/EMAT6680/Masson/6690/Instructional_Unit_plan/Week1/week1_day3.html
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