This cluster includes the following access points.
| Access Point Number |
Access Point Title |
| MAFS.912.G-SRT.1.AP.1a: | Given a center and a scale factor, verify experimentally that when dilating a figure in a coordinate plane, a segment of the pre-image that does not pass through the center of the dilation, is parallel to its image when the dilation is performed. However, a segment that passes through the center remains unchanged. |
| MAFS.912.G-SRT.1.AP.2a: | Determine if two figures are similar. |
| MAFS.912.G-SRT.1.AP.2b: | Given two figures, determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides. |
| MAFS.912.G-SRT.1.AP.1b: | Given a center and a scale factor, verify experimentally that when performing dilations of a line segment, the pre-image, the segment which becomes the image is longer or shorter based on the ratio given by the scale factor. |
| MAFS.912.G-SRT.1.AP.3a: | Apply the angle-angle (AA) criteria for triangle similarity on two triangles. |
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Dilation of a Line: Factor of Two: | Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center. |
| Dilation of a Line: Factor of One Half: | Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center. |
| Dilation of a Line Segment: | Students are asked to dilate a line segment and describe the relationship between the original segment and its image. |
| Justifying a Proof of the AA Similarity Theorem: | Students are asked to justify statements of a proof of the AA Similarity Theorem. |
| Prove the AA Similarity Theorem: | Students will indicate a complete proof of the AA Theorem for triangle similarity. |
| Dilation of a Line: Center on the Line: | Students are asked to graph the image of two points on a line after a dilation using a center on the line and to generalize about dilations of lines when the line contains the center. |
| Describe the AA Similarity Theorem: | Students are asked to describe the AA Similarity Theorem. |
| Showing Similarity: | Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two quadrilaterals are similar. |
| The Consequences of Similarity: | 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. |
| To Be or Not To Be Similar: | Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two triangles are similar. |
| Name |
Description |
| Coding Geometry Challenge #23 & 24: | 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. |
| Transformation and Similarity: | 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. |
| How Much Proof Do We Need?: | Students determine the minimum amount of information needed to prove that two triangles are similar. |
| Congruence vs. Similarity: | 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. |
| Discovering Dilations: | This resource is designed to allow students to discover the effects of dilations on geometric objects using the free online tools in GeoGebra. |
| Dilation Transformation: | 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. |
| Geometry Problems: Circles and Triangles: | 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. |
| Geometry Problems: Circles and Triangles: | 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 and 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. |
| Patterns in Fractals: | This lesson is designed to introduce students to the idea of finding patterns in the generation of several different types of fractals. This lesson provides links to discussions and activities related to patterns and fractals as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one. |
Vetted resources students can use to learn the concepts and skills in this topic.
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
