1. Geometry Lesson 4.3A Similarity
T.2.G.1 Apply congruence (SSS …) and similarity (AA …) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification
M.3.G.4 Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)
M.3.G.5 Use properties of parallel lines and proportional reasoning to find the lengths of segments
CGT.5.G.5 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane
translations
reflections
rotations (90˚, 180˚, clockwise and counterclockwise about the origin)
dilations (scale factor)

2. Two polygons are similar if:
1. Corresponding angles are congruent
2. Corresponding sides are proportional

3. Similarity Ratio
Similarity Ratio – the ratio of the lengths of corresponding sides of similar triangles A B C 15 12 18 D E F 10 8 12

4. Similarity Ratio
Corresponding angles are congruent. (Mark congruent angles) A B C 15 12 18 D E F 10 8 12

5. Similarity Ratio
To write the similarity statement, keep the corresponding vertices in the same order: A B C 15 12 18 D E F 10 8 12

6. Similiarity Ratio
To write the similarity ratio, write the ratio of the corresponding sides and simplify. A B C 15 12 18 D E F 10 8 12
The similarity ratio is

7. Find the value of the variable.
Given: LOVE  MATH L E V O 8 16 x 12
1. Find the similarity ratio. z M H T A 6 9 y

8. Find the value of the variable (cont.)8 16 x 12
2. Write a proportion and solve for x. M H T A 6 z 9 y

9. Find the value of the variable (cont.)
3. Do the same for y and z. L E V O 8 16 x 12 M H T A 6 z 9 y

10. Use the given information to solve for x (round to the nearest tenth.)
Given ABC; || C B E D 3 x 7 15 A
1. Since || , then and
2. Therefore,

11. Use the given information to solve for x (round to the nearest tenth
Use the given information to solve for x (round to the nearest tenth.) Continued
Since , we can write a proportion to solve for x. C B E D 3 x 7 15 A

12. Use the given information to solve for x (round to the nearest tenth.)
Given ABC; || C B E D 4 9 6 x A

13. Use the given information to solve for x (round to the nearest tenth.)
Given a || b || c.
If parallel lines are cut by a traversal, the segments between the parallel lines are proportional. x 10 17 30 a c b
We can set up a proportion to solve for x.