Working through the lesson below with your child identify the characteristics of similar figures and create dilations of a given figure on a Cartesian plane.
Learning Takeaways: After this lesson, students will be able to:
This section will help your child to identify the characteristics of similar figures.
Similar Figures
Look at the examples below.
Example 1:
These rectangles are similar. They are the same shape. The sides are proportional. The angles all measure 90°.
Determining Proportional Sides
The lengths of the sides are proportional because lengths of each side of figure B are half of the corresponding side in figure A.
You can also create a proportion:
^{6}⁄_{4} = ^{3}⁄_{2} because the cross products are equal; (6 x 2) = (3 x 4)
Example 2
These triangles are scalene, which means each angle and side is a different measure. The angles of these similar triangles are 90°, 22.62°, and 67.68°.
These triangles are similar.
These figures are similar and have a size transformation of 3 (S_{3}).
The coordinates of ΔABC are: The coordinates for ΔFDE are: Triangle DEF is shown in red. 

Work through the two questions below with your child. The answers are shown but to try find them without looking!
Try It!
What are the coordinates of the second figure after a size transformation of 5 (S_{5})?
Solution
The coordinates of the similar figure are: (20 , 15); (20 , 15); (20, 20); (20 , 20)
Try It!
Draw a similar a similar figure with a size transformation of 2 (S_{2})?
Solution
The coordinates of the similar figure are: (2 , 6); (6 , 4); (8, 0); (6 , 0)
Click here to see the similar figure on the Cartesian plane (or mouse over the image)