General Information
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.
Test Item Specifications
Items may use geometric figures of any shape if the figure can be
deconstructed to form a triangle.
Neutral
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.
Items may be set in a real-world or mathematical context.
Items may require the student to use or choose the correct unit of
measure.
Sample Test Items (1)
| Test Item # | Question | Difficulty | Type |
| Sample Item 1 |  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. |
N/A | ETC: Editing Task Choice |
Related Courses
| Course Number1111 | Course Title222 |
| 1200400: | Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |
| 1206300: | Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) |
| 1206310: | Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |
| 1206320: | Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |
| 7912060: | Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated)) |
| 7912070: | Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 - 2023, 2023 and beyond (current)) |
| 1206315: | Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) |
| 1207300: | Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) |
| 7912065: | Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current)) |
Related Resources
Formative Assessments
| Name | Description |
| 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
| Name | Description |
| 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 | 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. |
| 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. |
| 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. |
Perspectives Video: Teaching Idea
| Name | Description |
| Measuring Height with Triangles and Mirrors | Reflect for a moment on how to measure tall objects with mirrors and mathematics. |
Problem-Solving Tasks
| Name | Description |
| 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. |
Student Resources
Problem-Solving Tasks
| Name | Description |
| 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. |
Parent Resources
Problem-Solving Tasks
| Name | Description |
| 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. |