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Example:Construct Quadrilateral given 3 Sides & 2 Angles

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In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or 'edges') and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad (meaning "four") and lateral (meaning "of sides").

Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed. Simple quadrilaterals are either convex or concave.

The interior angles of a simple quadrilateral add up to 360 degrees of arc.

(Our solved example in mathguru.com also uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

To construct a quadrilateral when 3 sides( x units, y units and z units) and 2 included angles are known

Draw a line segment AB = x units.

Make angles of 60and 90at A and B respectively.

With B as the centre and radius 4.5 units, we make an arc on the ray BX.

With A as the centre and radius 4 cm we make an arc on the ray AY.

Join the points D and C to obtain the required quadrilateral.

Obtain the required D and C to obtain the required Quadrilateral ABCD.