The Tangent Ratio - Getting Into It
Completion requirements
Lesson 1: The Tangent Ratio - Getting Into It
Triangles that are similar have the same shape, but not necessarily the same size or orientation. Similar triangles will always have the same three angle measures.
Similar Triangles
Triangles that have the same shape, with the same three angle measures |
The sides opposite equal angles in similar triangles are said to be corresponding. In the diagram below, the red sides correspond, the blue sides correspond, and the green sides correspond.
Getting Into It
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 check 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 adjust the triangles by moving points
and
. What do you notice about the relationship between the values of
and
?
- Try to explain the relationship you identified in part b.
-
Explain how
-
Suppose
.
-
What does this tell you about the size of
compared to the size of 
?
-
If
and
, 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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