Pythagorean Explorer

What is Pythagorean Explorer?

This applet allows users to study the nature of the Pythagorean Theorem. The applet provides the user with various types of triangles of varying difficulty. For each right triangle two sides are given and the right angle is labeled. The user is to calculate the measure of the unknown side.

The Pythagorean Theorem states that the hypotenuse squared is equal to the sum of the squares of the legs of a right triangle.

C = the hypotenuse

A = one leg

B = the other leg.

How Do I Use This Activity?

This applet allows the viewer to calculate the length of one side of a triangle using the Pythagorean Theorem.

Controls and Output

  • Select the appropriate difficulty level by clicking on the level button. Once the correct level has been chosen, click the new triangle button to display a triangle with the selected difficulty level settings.
  • One side of the right triangle is labeled with an "X". The "X" designates which side of the triangle the viewer is to calculate the measure of using the Pythagorean Theorem.
  • Input your solution into the input box and click the "Check Answer" button.
  • To try out the Pythagorean Theorem on another triangle click the "New Triangle" button.

Scoring

  • This activity will automatically record how successful you are at answering the questions. To view the score, press the Show Score button at the bottom of the activity and a pop-up window will appear with the scoreboard.
  • To close this pop-up window press the Close button or click back on the main window.
  • To pause the scoring, press the Active button at the bottom of the screen and it will change to a Paused button. To resume scoring, press the Paused button.
  • To reset the scoreboard, open the scoreboard using the Show Score button and then press the Reset button.

Because this activity randomly generates questions, a feature called Seed Random has been implemented that allows multiple users using different computers to work on the same problem. See Seed Random Help for instructions on using this feature.

Description

This applet allows the user to test their abilities using the Pythagorean Theorem. This activity would work well in same ability groups of one or two for about twenty-five minutes if you use the exploration questions and fifteen minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

  • practice the Pythagorean theorem
  • practice identifying the hypotenuse
  • practice the order of operations
  • practice solving one step equations

Standards Addressed

Grade 6

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student solves problems (including real-world situations) using perimeter, area, or volume.
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 7

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student solves problems (including real-world situations).
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 8

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student solves problems (including real-world situations).
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 9

  • Geometry

    • The student solves problems (including real-world situations).

Grade 10

  • Geometry

    • The student solves problems (including real-world situations).

Grade 7

  • Measurement and Geometry

    • 3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures

Sixth Grade

  • Geometry

    • Solve real-world and mathematical problems involving area, surface area, and volume.

Eighth Grade

  • Geometry

    • Understand and apply the Pythagorean Theorem.

Geometry

  • Similarity, Right Triangles, and Trigonometry

    • Define trigonometric ratios and solve problems involving right triangles

Grades 6-8

  • Geometry

    • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Grade 8

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 3: The learner will understand and use properties and relationships in geometry.

Introductory Mathematics

  • Data Analysis and Probability

    • COMPETENCY GOAL 3: The learner will understand and use properties and relationships in geometry.

  • Geometry and Measurement

    • COMPETENCY GOAL 2: The learner will use properties and relationships in geometry and measurement concepts to solve problems.
    • COMPETENCY GOAL 2: The learner will understand and use measurement concepts.

Technical Mathematics I

  • Geometry and Measurement

    • Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

  • Geometry and Measurement

    • Competency Goal 1: The learner will use properties of geometric figures to solve problems.

Textbooks Aligned

Grade Six

  • Covering and Surrounding

    • Investigation Six: Measuring Triangles

Grade Eight

  • Looking for Pythagoras

    • Investigation Three: The Pythagorean Theorem

Book 1

  • Module 1 - Tools for Success

    • Section 2: Sides of a Triangle
    • Section 2: Angles of a Triangle
    • Section 6: Improve your problem solving

  • Module 7 - Wonders of the World

    • Section 1: Customary Units for Area
    • Section 1: Area of a Parallelogram, Area of a Triangle

Book 2

  • Module 6 - Flights of Fancy

    • Section 4: Angles formed by a Transversal
    • Section 4: Angles in Triangles and Parallelograms

Book 3

  • Module 4 - Patterns and Discoveries

    • Section 5: Angles in Polygons
    • Section 6: Triangle Side Length Relationships

8th

  • Module 5 - Architects and Engineers

    • Section 3: Working with Triangles

Book 3

  • Roads and Ramps

    • Lesson 5: Exploring the Pythagorean Theorem
    • Lesson 6: Using the Pythagorean Theorem

Grade 8

  • Going the Distance

    • Pythagorean Theorem

  • Patterns and Figures

    • Triangular Numbers
    • Pascal's Triangle

  • Triangles and Patchwork

    • Similarity
    • Similar Triangles

Grade 7

  • Triangles and Beyond

    • Relationships between sides and angles of a triangle
    • Constructing Triangles
    • Congruence
    • Similarity

Be Prepared to

  • explain, in detail and with examples, which side of the triangle is the hypotenuse
  • explain how to solve the Pythagorean theorem for any unknown side length
  • explain inverse operations that may be used in solving the Pythagorean theorem.