Parallel Lines        Congruent Tri.        Congruent R. Tri.        Isosc. and Equil.    Quadrilaterals        Parallelograms        Ratios        Similar Polygons        Special Triangles       Circles        Area        Coordinate Geo.        Triangle Ineq.        Solids        Computer Fun

On this page, we hope to clear up problems that you might have with quadrilaterals.  Quadrilaterals are the most used shape (they cover everything from squares to trapezoids) in geometry except for the triangle.  Scroll down to start understanding quadrilaterals better! As noted above, a quadrilateral is any shape the has four sides.  Outlined below are four definitions that are good to always keep in mind when working with quadrilaterals. Consecutive angles are any two angles whose vertices are the endpoints of the same side.  (In the figure below, angle B and angle C are consecutive angles.) Consecutive sides are any two sides that intersect.  (In the figure, AB and BC are consecutive sides.) Opposite angles are any two angles that are not consecutive.  (In the figure, angle B and angle D are opposite angles.) Opposite sides are any two sides that are not consecutive.  (In the figure, AB and DC are opposite sides.) There is also a theorem in geometry that tells us that in all quadrilaterals, the sum of the measures of the angles is 360o.  This can be used in many situations, including problems where you need to find the measures of angles. 1. Problem: Find the measure of angle x. Solution: Use the given information to help you find any new information. Angle y = 80o because vertical angles are congruent. Angle z = 120o because it is supplementary to the 60o angle shown in the figure. You now know the measures of three of the four angles in the quadrilateral. The other, angle w can be found by using the theorem that tells us all quadrilaterals have a sum of angles that equals 360o. Set up an equation to do this. 360 = w + 75 + 80 + 120 Solve for w. w equals 85o. Angle x can now easily be found because it is supplementary to angle w, which you found above. Angle x = 95o Back to Top  Although you won't encounter many odd shapes, such as shapes with twelve sides, it can happen.  On most instances of this, you will need to find the sum of the measures of the angles.  There is a special theorem that says, if n is the number of sides of any polygon, the sum (S) of the measure of its angles is given by the formula - S = (n-2)180o. The figure and table below will help this theorem make more sense. ------------------------------------------------------------------- | Polygon | No. Sides | Total No. of | No. Triangles | Sum of | | | | Diagonals | Formed | Angle | | | | fr. 1 vertex | | Measures | ------------------------------------------------------------------- | Triangle | 3 | 0 | 1 | 180o | | Quad. | 4 | 1 | 2 | 360o | | Pentagon | 5 | 2 | 3 | 540o | | Hexagon | 6 | 3 | 4 | 720o | | . | . | . | . | . | | . | . | . | . | . | | . | . | . | . | . | | n-gon | n | n - 3 | n - 2 |(n-2)(180o)| ------------------------------------------------------------------- Back to Top  Take the Quiz on quadrilaterals.  (Very useful to review or to see if you've really got this topic down.)  Do it!