Try to draw the quadrilateral that is asked by moving the points A, B, C and D over the grid (click and drag the mouse). Notice that the quadrilateral vertices can only be placed on points with integer coordinates. To check your answer, click on the “Check my answer!” button. If you don't obtain success in 4 attempts, the software will show you an answer (but it will subtract points of your score).

Below the applet, there are check boxes that allow showing/hiding diagonals, line bisectors and angle bisectors of the quadrilateral. The various definitions considered by the game can be found in the bottom of this page.

Score: 0

Challenge 1 de 19: Draw a non convex polygon!

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In mathematics, there are terms with no consensus about their definitions: different people use the same mathematical term with different meanings. This is the case of the term “polygon”. In the software of this activity, we use the definitions given below. They can be different from the definitions used in the book you're studying.

Definition (Polygonal Line). A polygonal line is a planar figure formed by a sequence of points A1, A2, ..., An and the segments A1A2, A2A3, ..., An−1An. The points are the vertices of the polygonal line and the segments are their sides. If An = A1, we say that the polygonal line is closed.

Definition (Polygon). A polygon is a polygonal line with the following properties: (a) it is closed, (b) each one of its vertices is an end of two sides and (c) two sides with a common end are not collinear.

Definition (Simple Polygon). A polygon P is simple provided the only points of the plane that belong to two edges of P are the vertices of P. Simple polygons also are called of Jordan's polygons, because the Jordan's curve theorem can be used to demonstrate that such a polygon divides the plan in two regions, the interior region inside of it and the exterior region outside of it.

Definition (Convex Polygons). We say that a simple polygon is convex if its interior C is convex, i.e., when any line segment joining two points of C is completely contained in C. A convex polygon is always contained in one of the half-planes determined by the straight lines that contain its sides.

Definition (Quadrilateral). A quadrilateral is a polygon with four sides.

Definition (Parallelogram). A parallelogram is a convex quadrilateral whose opposite sides are parallels and congruents.

Definition (Rhombus). A rhombus is a parallelogram which all sides are congruents.

Definition (Kite). A kite is a convex quadrilateral with two adjacent sides having the same length, say a, and the other two sides (adjacents) also having the same length, say b. The rhombus is a special case of kite (where a = b).

Definition (Rectangle). A rectangle is a convex quadrilateral with four right angles.

Definition (Square). A square is a rectangle that also is a rhombus, in other words, a square is a convex quadrilateral with four right angles and four congruent sides.

Definition (Trapezium). A trapezium is a convex quadrilateral with parallel opposite sides. The parallel opposite sides are called bases and the other two are called laterals. A trapezium is called isosceles if its laterals are congruents. A trapezium is called scalene if its laterals are not congruents. A trapezium is called right if it has at least two right angles.

Definition (Diagonal of a Polygon). A diagonal of a polygon is any straight line segment joining two non consecutive vertices of the polygon.

Definition (Orthodiagonal Quadrilateral). A quadrilateral is orthodiagonal if its two diagonals are perpendicular.

Definition (Cyclic Polygon). A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. A polygon is cyclic if all its vertices belong to the same circle, that is, if there is a circle which circumscribe the polygon.

Definition (Inscriptible Polygon). A polygon is inscriptible if its sides are tangent to a same circle. In this situation, we say that the polygon circumscribes the circle.

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Responsible: Humberto José Bortolossi.
Idealization: Thamiris Franckini Paiva and Humberto José Bortolossi.
Programming: Thamiris Franckini Paiva and Humberto José Bortolossi.
Revision: Alberto Rodrigues Paiva, Carlos Eduardo Castaño Ferreira, Igor Bromonschenkel Brandão, Thamiris Franckini Paiva and Humberto José Bortolossi.
This activity was built with the free and multi-platform dynamic mathematics software GeoGebra.

Game of the Classification of quadrilaterals Versão 1.0
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