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:
- Identify the characteristics of similar figures
- Create a dilation of a given figure on a Cartesian plane
This section will help your child to identify the characteristics of similar figures.
- Are the same shape
- Have proportional sides
- Have the same angle measures
Look at the examples below.
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)
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.
- Both figures are right, scalene triangles.
- The sides are proportional. The larger triangle's sides are twice as large as the smaller triangle's.
- The angles are equal.
Creating a Dilation
These figures are similar and have a size transformation of 3 (S3).
The coordinates of ΔABC are:
A = (2,4) B = (-6,2) C = (-2,-2)
Triangle DEF has a size transformation of 0.5 (S0.5). That means you multiply the coordinates of ΔABC by 0.5.
The coordinates for ΔFDE are:
F = (1,2) D = (-3,1) E = (-1,-1)
Triangle DEF is shown in red.
More Dilation Examples
Work through the two questions below with your child. The answers are shown but to try find them without looking!
What are the coordinates of the second figure after a size transformation of 5 (S5)?
- Find the coordinates of the figure ABCD shown on the Cartesian Plane.
- The coordinates are: A= (-4,3), B = (4,3) , C = (-4,-4), D = (4,-4)
- Multiply both numbers in the coordinate pair by 5
The coordinates of the similar figure are: (-20 , 15); (20 , 15); (-20, -20); (20 , -20)
Draw a similar a similar figure with a size transformation of 2 (S2)?
- Find the coordinates of figure JBXE
- Multiply these coordinates by 2
- Redraw the figure using the new coordinates
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)