The topic Constructing 2D figures appears under the 7th grade (U.S.) Math Mission. This exercise describes quadrilaterals and explores some congruency theorems for them.

Types of Problems

There are two types of problems in this exercise:

  1. Draw the quadrilateral and tell whether another can exist: This problem has the user draw a quadrilateral satisfying certain conditions on a coordinate axes. After drawing the figure, the user is also asked to determine if the figure drawn is unique or if another could exist.

    Draw the quadrilateral and tell whether another can exist

  2. Tell whether another figure could exist: This problem is much like the previous, except this time the user is not required to actually draw the shape.

    Tell whether another figure could exist


Geometric reasoning is important for this problem but there are not a good set of rules to follow in any standard textbook. Knowledge of the different quadrilaterals is the best point of reference to complete this exercise.

  1. There is no collection of quadrilateral congruency theorems so these problems are most like done efficiently by drawing them on paper or visualizing what is occurring.

Real-life Applications

  1. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.
  2. Measurement is important for taking proper medicine. If one has an illness (whether serious or minor) they need to take their medicine and take it in the proper amount. If they take too little or too much then they are not going to get the proper benefit from it.

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