Trapezoid: Triangle, Diagonals, Midpoints, Bases. Level: High School, SAT Prep, College

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


 


Proposition
Given a triangle ABC and a trapezoid ADEC (DE // AC), as shown. AE and CD meet at F, and BF meets DE and AC at N and M respectively. Prove that M and N are the midpoints of AC and DE respectively.

 

Interactive Geometry: 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 interactive 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, C and D, 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.

 

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