### Remarks

**Geometry - Fluency Recommendations**

Fluency with the triangle congruence and similarity criteria will help students throughout their investigations of triangles, quadrilaterals, circles, parallelism, and trigonometric ratios. These criteria are necessary tools in many geometric modeling tasks.

**Subject Area:**Mathematics

**Grade:**912

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

**Cluster:**Level 3: Strategic Thinking & Complex Reasoning

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

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.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Items may use geometric figures of any shape if the figure can be

deconstructed to form a triangle.**Calculator :**Neutral

**Clarification :**

Students will use congruence criteria for triangles to solve problems.Students will use congruence criteria for triangles to prove

relationships in geometric figures.Students will use similarity criteria for triangles to solve problems.

Students will use similarity criteria for triangles to prove relationships

in geometric figures.**Stimulus Attributes :**

Items may be set in a real-world or mathematical context.**Response Attributes :**

Items may require the student to use or choose the correct unit of

measure.

**Test Item #:**Sample Item 1**Question:**There are three highlights in the paragraph to show blanks in the proof. For each highlight, click on the word or phrase to fill in the blank.

**Difficulty:**N/A**Type:**ETC: Editing Task Choice

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## MFAS Formative Assessments

Students are asked to decide if a basketball goal is regulation height and are given enough information to determine this using similar triangles.

Students are given a diagram of a county fair and are asked to use similar triangles to determine distances from one location of the fair to another.

Students are asked to prove a specific diagonal of a rhombus bisects a pair of angles.

Students are asked locate a pair of similar triangles in a diagram, explain why they are similar, and use the similarity to find two unknown lengths in the diagram.

Students are asked to locate a pair of similar triangles in a diagram, explain why they are similar, and use the similarity to find an unknown length in the diagram.

## Student 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

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

Type: Problem-Solving Task

## 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

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

Type: Problem-Solving Task