Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Number:**MAFS.912.G-SRT.2

**Title:**Prove theorems involving similarity. (Geometry - Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**912

**Domain-Subdomain:**Geometry: Similarity, Right Triangles, & Trigonometry

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Perspectives Video: Teaching Idea

## Presentation/Slideshow

## Problem-Solving Tasks

## Professional Development

## Tutorials

## Video/Audio/Animation

## Virtual Manipulative

## Student Resources

## Original Student Tutorial

Use properties, postulates, and theorems to prove a theorem about a triangle. In this interactive tutorial, you'll also learn how to prove that a line parallel to one side of a triangle divides the other two proportionally.

Type: Original Student Tutorial

## Presentation/Slideshow

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra and addresses the following national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning: 1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2) Use visualization, spatial reasoning, and geometric modeling to solve problems; 3) Understand and apply basic and advanced properties of the concepts of geometry; and 4) Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups. I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers.

Type: Presentation/Slideshow

## Problem-Solving Tasks

This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

Type: Problem-Solving Task

This task involves a reasonably direct application of similar triangles, coupled with a moderately challenging procedure of constructing a diagram from a verbal description.

Type: Problem-Solving Task

Using a triangle with line through it, students are tasked to show the congruent angles, and conclude if one triangle is similar to the other.

Type: Problem-Solving Task

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Type: Problem-Solving Task

## Tutorials

This video demonstrates Bhaskara's proof of the Pythagorean Theorem.

Type: Tutorial

This video visually proves the Pythagorean Theorem using triangles and parallelograms.

Type: Tutorial

This video shows a proof of the Pythagorean Theorem using similar triangles.

Type: Tutorial

## Video/Audio/Animation

This resource gives an animated and then annotated proof of the Pythagorean Theorem.

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Tasks

This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

Type: Problem-Solving Task

This task involves a reasonably direct application of similar triangles, coupled with a moderately challenging procedure of constructing a diagram from a verbal description.

Type: Problem-Solving Task

Using a triangle with line through it, students are tasked to show the congruent angles, and conclude if one triangle is similar to the other.

Type: Problem-Solving Task

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Type: Problem-Solving Task