Triangle and Squares Theorem 1: Triangle and Squares. Level: High School, SAT Prep, College



 


Draw squares ABDE and BCFG on sides AB and BC of a triangle ABC. Prove the following:

  • CD and AG are congruent and perpendicular

  • CD, AG, and EF are concurrent in H

  • EF is bisector of angle GHC.

 

Click the red button () on the figure to start the animation. Drag points A, C, and line AC to change the figure. Press P and click the left mouse button to start the step by step construction.



Dynamic Geometry or Interactive Geometry Software  are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. One starts construction by putting a few points and using them to define new objects such as lines, circles or other points. After some construction is done, one can move the points one started with and see how the construction changes. You can alter the figure dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand.

This page uses the TracenPoche dynamic geometry software and requires Adobe Flash player 7 or higher. TracenPoche is a project of Sesamath, an association of French teachers of mathematics.

Instruction to explore the dynamic figure:

  • Animation. Click the red button to start/stop animation

  • Manipulate. Drag points A and C, and line AC to change the figure.

  • Step-by-Step construction. Press P and click the left mouse button on any free area of the figure above to show the step-by-step bar and click 'Next Step' button () to start the construction step-by-step:

     
    Hide the step-by-step bar by using again the combination P + click left mouse.

 

 

Triangle and Square Theorem. Elearning, Online Tutoring

 

 

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Last updated: August 1, 2009