Similar Polygons - Getting Into It
Completion requirements
Lesson 1: Getting Into It - Similar Polygons
Getting into It
Repeat the Getting Into It investigation from Chapter 4, Lesson 1 - The Tangent Ratio. The activity is provided again below.
Investigation
The following applet explores a relationship that is true for all similar triangles. If you are unable to access the applet, skip ahead to the Alternate Investigation on the next page.
Applet: Similar Triangles
29 January 2014, Created with GeoGebra
The two triangles shown in the applet are similar and both include a right angle. They can be adjusted by changing the scale factor and by moving the points
and 
. Use the applet to answer the following questions.
-
Knowing that
is similar to 
, what relationship do you expect between angles
and 
, and
and 
? Turn on "Show Angles" to confirm your prediction.
-
Turn off "Show Angles" and turn on "Show Ratios" so the ratios
and 
are shown.
-
Explain how
and
are calculated.
-
Keep an eye on the ratios as you change the triangles by moving points
and
. What do you notice about the relationship between the values of
and
?
- Try to explain the relationship you noticed in part b.
-
Explain how
-
Suppose
.
-
What does this tell you about the size of
compared to the size of 
?
-
If
, while
, what must be the length of 
? Try to answer without using the applet.
-
What does this tell you about the size of
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