This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Pythagorean Theorem Proof: | Students are asked to prove the Pythagorean Theorem using similar triangles. |
| Geometric Mean Proof: | Students are asked to prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse. |
| Converse of the Triangle Proportionality Theorem: | Students are asked to prove that if a line intersecting two sides of a triangle divides those two sides proportionally, then that line is parallel to the third side. |
| Triangle Proportionality Theorem: | Students are asked to prove that a line parallel to one side of a triangle divides the other two sides of the triangle proportionally. |
| 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. |
| 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. |
| Proofs of the Pythagorean Theorem: | This lesson is intended to help you assess how well students are able to produce and evaluate geometrical proofs. In particular, this unit is intended to help you identify and assist students who have difficulties in:
- Interpreting diagrams.
- Identifying mathematical knowledge relevant to an argument.
- Linking visual and algebraic representations.
- Producing and evaluating mathematical arguments.
|
| 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.
This activity is meant to be a review activity after similar triangles have already been taught, and can be used as a summative assessment. |
| 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. |
| 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. |
| Joining two midpoints of sides of a triangle: | 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. |
| Unit Squares and Triangles: | This problem solving task asks students to find the area of a triangle by using unit squares and line segments. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
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. |
| Joining two midpoints of sides of a triangle: | 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. |
| Unit Squares and Triangles: | This problem solving task asks students to find the area of a triangle by using unit squares and line segments. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
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. |
| Joining two midpoints of sides of a triangle: | 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. |
| Unit Squares and Triangles: | This problem solving task asks students to find the area of a triangle by using unit squares and line segments. |
