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Aim: How can we review similar triangle proofs?

+. Aim: How can we review similar triangle proofs?. -. +. +. =. +. HW: Worksheet Do Now: Solve the following problem: The length of the sides of a triangle are 9, 15, and 21. If the length of the shortest side of a similar triangle is 12, find the length of its longest side. -. =. -.

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Aim: How can we review similar triangle proofs?

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  1. + Aim: How can we review similar triangle proofs? - + + = + HW: Worksheet Do Now: Solve the following problem: The length of the sides of a triangle are 9, 15, and 21. If the length of the shortest side of a similar triangle is 12, find the length of its longest side. - = -

  2. Answer 28 21 9 28 12 15 20

  3. Similar figures- two figures that have the same shape but may be the same size. In proportion 10 5 8 4 3 6

  4. For two triangles to be similar,  their corresponding angles must be congruent and the lengths of their corresponding sides must be in a ratio, and therefore be in proportion.

  5.     For example : If side AB of triangle ABC is 6 inches long and side DE of triangle DEF is 9 inches long. Then the two sides are in a 2 to 3 ratio which is their ratio of similitude.  Ratio of similitude- the ratio of the two corresponding sides of the two similar triangles. 

  6. If two triangles are similar the following can be concluded about them: • Their corresponding angles are congruent  - The length of the corresponding sides are in proportion

  7. Example: The length of the sides of a smaller triangle are 6,8,10. The lengths of the sides of a larger triangle are 9, 12 and 15. Show which corresponding angles are congruent as well as the ratio of similitude between the two triangles. 

  8. Answer: 2:3 10 6 8 15 9 12

  9. To prove the two triangles similar:  • Two triangles are similar when at least two of the angles of one triangle can be proven congruent to the corresponding two angles of another triangle. • To do this use the: Angle Angle Postulate of similarity- which states that two triangles are similar if two angles of one triangle are congruent to the corresponding angles of the other triangle.

  10. Problem#1

  11. Statement Reason

  12. Once two triangles are proven similar, a proportion involving the lengths of corresponding sides can be used as a reason in proving proportions and can be stated as  " Lengths of corresponding sides of a similar triangle are in proportion."

  13. Problem#2

  14. Statement Reason

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