Standard #: MAFS.912.G-SRT.1.2 (Archived Standard)

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two quadrilaterals are similar.

Students are given the definition of similarity in terms of similarity transformations and are asked to explain how this definition ensures the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two triangles are similar.

This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. Students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Using non-rigid motions (dilations), students learn how to show that two polygons are similar. Students will write coordinate proofs confirming that two figures are similar.

Students will learn the difference between congruence and similarity of classes of figures (such as circles, parallelograms) in terms of the number of variable lengths in the class. A third category will allow not only rigid motions and dilations, but also a single one-dimensional stretch, allowing more classes of figures to share sufficient common features to belong.

Students identify dilations, verify that polygons are similar, and use the dilation rule to map dilations. Task cards are provided for independent practice. The PowerPoint also includes detailed illustrations for constructing a dilation using a compass and a straight edge.

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties:

• Solving problems by determining the lengths of the sides in right triangles.
• Finding the measurements of shapes by decomposing complex shapes into simpler ones.

The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

The "machine" generates 5000 points based upon a random selection of points. Each point is chosen iteratively to be a particular fraction of the way from a current point to a randomly chosen vertex. For carefully chose fractions, the results are intriguing fractal patterns, belying the intuition that randomness must produce random-looking outputs.

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.

This informational text resource is intended to support reading in the content area. The article indicates that traditional geometry does not suffice in describing many natural phenomena. The use of computers to implement repeated iterations can generate better models. Offered by IBM, this text can be used in a high school geometry class to demonstrate applications of similarity and to illustrate important ways that geometry can be used to model a wide range of scientific phenomena.

This is an interactive model that demonstrates how different light levels effect the size of the pupil of the eye. Move the slider to change the light level and see how the pupil changes.

Students will analyze the perimeters of stages of the Koch Snowflake and note that the perimeter grows by a factor of 4/3 from one stage to the next. This means that the perimeter of this figure grows without bound even though its area is bounded. This effect was noted in the late 1800's and has been called the Coastline Paradox.

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.