Lesson on similar triangles

1. Similar Triangles G.G.44 Establish similarity of triangles using the following theorems: AA, SAS, SSS G.G. 45 Investigate, justify, and apply theorems about similar triangles

4. In order to set up the proportions, you need to know what sides are corresponding. Just like congruent triangles, the corresponding sides are two sides that are between the same angles. 50º 50º 100º 100º 30º 30º A B C D E F So, since side AB is between the angles of 100º and 50º, you need to identify the side in the other triangle that is between the same angles! We would say that AB is similar to DE, BC is similar to EF, and CA is similar to FD.

5. Identify the similar sides of the following: 40º 60º 80º 80º 40º 60º G W Y N R L

6. Now, when you’re setting up proportions for similar triangles, remember that if you put the first triangle in the numerator, it has to ALWAYS be in the numerator for your equations. G W Y N R L

8. Example 2: Triangle NTE is similar to triangle KLA. If TE=16, EN=24, and AK=3, what is the length of LA? 48 = 24x 2 = x N T E K L A 16 24 3 x

9. The length of the shortest side of a triangle is 12, and the length of the shortest side of a similar triangle is 4. If the longest side of a triangle is 15, what is the longest side of a similar triangle? Cross-multiply to solve! 12x = 60 x = 5