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 + - + - - + + = =
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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.
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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
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3
4
108
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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.
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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."