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Circle the ways that Triangles can be congruent:

Circle the ways that Triangles can be congruent:. SSS SAS SSA AAA AAS. Proving Triangles Similar. Geometry Unit 11, Day 6 Ms. Reed. Similar Triangles. Similar Triangles have congruent angles a similarity ratio between the corresponding sides. The sign for similarity is ~.

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Circle the ways that Triangles can be congruent:

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  1. Circle the ways that Triangles can be congruent: • SSS • SAS • SSA • AAA • AAS

  2. Proving Triangles Similar Geometry Unit 11, Day 6 Ms. Reed

  3. Similar Triangles • Similar Triangles have • congruent angles • a similarity ratio between the corresponding sides. • The sign for similarity is ~

  4. In groups of 2: • We will be discovering ways to prove triangles similar. • You will need: calculator ruler protractor scrap paper

  5. Is AA a way to prove triangles similar? • In your groups, each draw a large triangle with a 50° and a 60° angle • Measure the sides of the triangle to the nearest 1/16 • Find the ratio of the corresponding sides • ARE THE TRIANGLES SIMILAR?

  6. Is SAS a way to prove triangles similar? • In your groups, each person draw an angle that is 90° • Using a similarity ratio of ½, proportionally draw the 2 sides that include the angle. • ARE THE TRIANGLES SIMILAR?

  7. Is SSS a way to prove triangles similar? • With a partner, pick the lengths of both triangles with a similarity ratio of ½. **Use a special right triangle to keep in easier** • Draw each of the triangles. **Start with a 90° angle. • Measure the angles of the triangles. • ARE THE TRIANGLES SIMILAR?

  8. Triangle Similarity • We can use AA, SAS, and SSS to prove triangles congruent.

  9. Example 1 • Are these triangles similar? Why? 45 45

  10. Example 2 • Are these triangles similar? Why? 8 8 6 6 9 12

  11. Example 3 • Are these triangles similar? Why? 9 14 7 18

  12. Solving for a missing side: • How are we going to find x?! • Set up a proportion! 5 12 4 x

  13. 5 12 4 x Solving for a missing side: What side of one triangle corresponds with what side of the other? 12 = x4 5 x = 15

  14. Example 4 • Find the value of x 9 8 x 6

  15. Homework • Work Packet: Triangle Similarity

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