Lesson 9Side Length Quotients in Similar Triangles
Learning Goal
Let’s find missing side lengths in triangles.
Learning Targets
I can decide if two triangles are similar by looking at quotients of lengths of corresponding sides.
I can find missing side lengths in a pair of similar triangles using quotients of side lengths.
Lesson Terms
- similar
Warm Up: Two-three-four and Four-five-six
Problem 1
Triangle
Activity 1: Quotients of Sides Within Similar Triangles
Problem 1
Your teacher will assign you one of the three columns in the second table.
Triangle
Find the side lengths of triangles
, , and . Record them in the table. triangle
scale factor
length of short side
length of medium side
length of long side
Your teacher will assign you one of the three columns. For all four triangles, find the quotient of the triangle side lengths assigned to you and record it in the table. What do you notice about the quotients?
triangle
(long side)
(short side) (long side)
(medium side) (medium side)
(short side) or 1.75 Compare your results with your partners’ and complete your table.
Are you ready for more?
Problem 1
Triangles
Activity 2: Using Side Quotients to Find Side Lengths of Similar Triangles
Problem 1
Triangles
Lesson Summary
If two 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 short and medium length sides of the small and large triangle.
small triangle | large triangle | |
---|---|---|
medium side | ||
short side | ||
(medium side) |
The lengths of the medium side and the short side are in a ratio of
This is true for all similar polygons; the ratio between two sides in one polygon is the same as the ratio of the corresponding sides in a similar polygon.
We can use these facts to calculate missing lengths in similar polygons. For example, triangles
In triangle