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 = =

Answer

Similar figures- two figures that have the same shape but may be the same size. In proportion

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.

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.

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

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.

Answer: 2:3

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.

Problem#1

Statement Reason

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."

Problem#2

Statement Reason