Unit 2, Lesson 9
Side Length Quotients in Similar Triangles
Grade 8
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Triangle
The scale factors for the dilations that show triangle
| triangle | scale factor | length of short side |
length of medium side |
length of long side |
|---|---|---|---|---|
| 1 | 4 | 5 | 7 | |
| 2 | ||||
| 3 | ||||
| triangle | (long side) |
(long side) |
(medium side) |
|---|---|---|---|
|
|
|
|
|
What do you notice about the quotients?
Triangles
The side lengths of the triangles all have the same units. Find the unknown side lengths.
Three triangles. Vertices capital A, B C. Sides B C and A, C length 4. Side A, B length lower-case c. Vertices capital I H G. Side I G length lower-case h. Side I H length fraction 12 over 5. Side H G length fraction 6 over 5. Vertices capital D E F. Side E F 5, Side F D length lower-case e, side E D length lowercase d.
If 2 polygons are similar, then the side lengths in one polygon are multiplied by the same scale factor to give the corresponding side lengths in the other polygon.
For these triangles the scale factor is 2:
Here is a table that shows relationships between the lengths of the short and medium sides of the 2 triangles.
| small triangle | large triangle | |
|---|---|---|
| medium side | 4 | 8 |
| short side | 3 | 6 |
| (medium side) |
The lengths of the medium side and the short side are in a ratio of
We can use these facts to calculate missing lengths in similar polygons. For example, triangles
Since side