MAFS.912.G-SRT.2.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Clarifications

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.
General Information
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
Assessed: Yes
Test Item Specifications

  • 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.
Sample Test Items (1)
  • 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

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022 (current), 2022 and beyond)
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
7912065: Access Geometry (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-SRT.2.AP.5a: Apply the criteria for triangle congruence and/or similarity (angle-side-angle [ASA], side-angle-side [SAS], side-side-side [SSS], angle-angle [AA] to determine if geometric shapes that divide into triangles are or are not congruent and/or can be similar.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 1 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 3 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 2 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Formative Assessments

County Fair:

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.

Type: Formative Assessment

Basketball Goal:

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

Type: Formative Assessment

Prove Rhombus Diagonals Bisect Angles:

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

Type: Formative Assessment

Similar Triangles - 2:

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.

Type: Formative Assessment

Similar Triangles - 1:

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.

Type: Formative Assessment

Lesson Plans

What's the Problem:

Students solve problems using triangle congruence postulates and theorems.

Type: Lesson Plan

How Do You Measure the Immeasurable?:

Exploring dangerous caves and discovering craters on Mars are just a few of the topics students will investigate as they use similar triangles to determine inaccessible measurements.

Type: Lesson Plan

Let's Prove the Pythagorean Theorem:

Students will use Triangle Similarity to derive the proof of the Pythagorean Theorem and apply this method to develop the idea of the geometric mean with respect to the relationships in right triangles.

Type: Lesson Plan

Altitude to the Hypotenuse:

In this lesson, students discover what happens when the altitude to the hypotenuse of a right triangle is drawn. They learn that the two triangles created are similar to each other and to the original triangle. They will learn the definition of geometric mean and write, as well as solve, proportions that contain geometric means. All discovery, guided practice, and independent practice problems are based on the powerful altitude to the hypotenuse of a right triangle.

Type: Lesson Plan

Modeling: Rolling Cups:

This lesson unit is intended to help you assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables and develop experimental and analytical models of a physical situation.

Type: Lesson Plan

Solving Geometry Problems: Floodlights:

This lesson unit is intended to help you assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in making a mathematical model of a geometrical situation, drawing diagrams to help with solving a problem, identifying similar triangles and using their properties to solve problems and tracking and reviewing strategic decisions when problem-solving.

Type: Lesson Plan

Mirror, Mirror on the ... Ground?:

This activity allows students to go outdoors to measure the height of objects indirectly. Similar right triangles are formed when mirrors are placed on the ground between the object that needs to be measured and the student observing the object in the mirror. Students work in teams to measure distances and solve proportions.

This activity is meant to be a review activity after similar triangles have already been taught, and can be used as a summative assessment.

Type: Lesson Plan

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.

Type: Lesson Plan

Perspectives Video: Teaching Idea

Measuring Height with Triangles and Mirrors:

Reflect for a moment on how to measure tall objects with mirrors and mathematics.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Bank Shot:

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

Exstensions, Bisections and Dissections in a Rectangle:

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

Unit Squares and Triangles:

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

Type: Problem-Solving Task

MFAS Formative Assessments

Basketball Goal:

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

County Fair:

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.

Prove Rhombus Diagonals Bisect Angles:

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

Similar Triangles - 1:

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.

Similar Triangles - 2:

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

Vetted resources students can use to learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Bank Shot:

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

Exstensions, Bisections and Dissections in a Rectangle:

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

Unit Squares and Triangles:

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

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Bank Shot:

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

Exstensions, Bisections and Dissections in a Rectangle:

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

Unit Squares and Triangles:

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

Type: Problem-Solving Task