Dilations and Similarity

8th - 10th

In this dilations and similarity instructional activity, pupils solve 10 different problems that include various dilations. First, they determine the scale factor of dilations found in the illustrated graphs. Then, everyone determines the coordinates of the image of a point under a dilation with the center at the origin of scale factor.

Resource Details

Instructional Design
Skills Practice

Dilation and Area

Students investigate dilations.  In this geometry lesson, students investigate the relationship between the area of a geometric shape and the dilation factor.  The use of geometry software allows for conjecture and verification.

Dilations in the Plane

In this geometry lesson, students collect and analyze data as they investigate relationships between the pre-image and the image of a triangle. They investigate angle measures, side lengths, and the dilation factor. The dynamic nature of Cabri Jr. allows students to form and verify conjectures regarding dilations.


In this triangles instructional activity, 10th graders solve and graph 8 different problems that include various transformations. First, they write a rule for the composition of a dilation of a scale factor. Then, students determine whether a graphed triangle is a reflection of another. They also determine the single transformation that accomplishes given triangle transformations.

Studying the Properties of Figures Created through a Dilation

In this geometry activity, students walk through several exercises to determine the effect of dilation when the scale factor is less than 1, greater than 1, or equal to 1 as well as the effect on the lengths, area, and vertices of a polygon. There are 55 questions and several pages of blank graph paper.


In this dilations worksheet, 10th graders solve and complete 10 different problems related to various dilations. First, they determine they coordinates of a point under a dilation of scale factor with the center at the origin. Then, students determine the scale factor of the dilation with center at the origin if a given point moves. They also determine whether the graph shows the correct dilation.


In this transformations worksheet, 10th graders solve and complete 10 various types of problems. First, they draw the graph of a parabola for all values of x in the interval. Then, students graph and state the coordinates of a triangle. They also write an equation for a given image under the composition of translations.

Similar Triangles

Although a rather complicated topic, this video manages to clearly explain the concept of solving problems involving similar triangles. It employs problem solving to determine whether two figures are similar triangles. In addition, it provides guidance for finding the anglesÕ values. Tip: the presentation finishes prior to solving the final problem. Furthermore, this is the first part of a series on similar triangles.

Solving a Quadratic by Factoring

Solving quadratics by factoring is the main concept in this video. Several examples are shown with positive numbers and with negative numbers. The instructor demonstrates how to set the factored equation to zero to solve the quadratic. He uses a graph to enhance his explanation.

How Do You Find a Scale Factor in Similar Figures?

Three angles of one triangle are equal to the corresponding angles in another triangle. Use a ratio of corresponding sides to find the scale factor. Actually, there are two scale factor values. The instructor will explain how to get both values.

Dilations in the Plane

Tenth graders investigate dilations and explore the dilation transformation before investigating the properties of a dilation using Cabri Jr. Students extend the concept of dilatation to the coordinate plane.

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