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

Standard #: MAFS.912.G-SRT.2.5Archived Standard
Standard Information
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
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
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.
  • 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.
  • Prove Rhombus Diagonals Bisect Angles # Students are asked to prove a specific diagonal of a rhombus bisects a pair of angles.
  • 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.
  • 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.
Lesson Plans
  • What's the Problem # Students solve problems using triangle congruence postulates and theorems.
  • How Do You Measure the Immeasurable? # Students will use similar triangles to determine inaccessible measurements. Examples include exploring dangerous caves and discovering craters on Mars.
  • 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.
  • Altitude to the Hypotenuse # Students will 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.
  • 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.
  • Solving Geometry Problems: Floodlights # Assess how well students can identify and use geometrical knowledge to solve a problem. Specifically, identify similar triangles and use their properties to prove and solve problems. Students will also be provided with examples of other students’ work to critique. The lesson closes with a whole-group discussion where students explain and compare the alternative approaches they have seen and used.
  • 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 can be used as a review or summative assessment after teaching similar triangles.
  • Patterns in Fractals # This guided discovery lesson introduces students to 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.
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.
  • Extensions, 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.
  • Unit Squares and Triangles # This problem solving task asks students to find the area of a triangle by using unit squares and line segments.
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.
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