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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Answer

21

15

912

28

20

28

Similar figures- two figures that have the same shape but may be

the same size.

In proportion

5

3

4

108

6

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. 

159

12

6

8

10

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