4. A SQUARE is a rectangle having its adjoiningsides equal.a.b.c.d.e.ABCD is a square.AC and BD are diagonals.O is the geometric center of the square.AO = OC = OB = OD.O is equidistant from all sides.A square may be constructed if one side isknown.POLYGONSA polygon is a many-sided plane shape. It is said tobe regular if aIl sides are equal and irregular when theyare not. Only regular polygons are described here.Regular PolygonsTriangles and quadrilaterals fit the description of apolygon and have been covered previously. Three othertypes of regular polygons are shown in the illustration.Each one is inscribed in a circle. This means that allvertices of the polygon lie on the circumference of thecircle.Note that the sides of each of the inscribed polygonsare actually equal chords of the circumscribed circle.Since equal chords subtend equal arcs, by dividing thecircumference into an equal number of arcs, a regularpolygon may be inscribed in a circle. Also note that thecentral angles are equal because they intercept equalarcs. This gives a basic rule for the construction ofregular polygons inscribed in a circle as follows:To inscribe a regular polygon in a circle, createequal chords of the circle by dividing the circumferenceinto equal arcs or by dividing the circle into equal centralangles.Dividing a circle into a given number of parts hasbeen discussed, so construction should be no problem.Since there are 360 degrees around the center of thecircle, you should have no problem in determining thenumber of degrees to make each equal central angle.Problem:What is the central angle used to inscribe a pentagon ina circle?Solution:360°5 slides= 72° in each circleMethods for Constructing PolygonsThe three methods for constructing polygons de-scribed here are the pentagon, the hexagon, and theoctagon.The PENTAGONis a method to develop the lengthof a side and departs from the rule given. Radius PB hasbeen bisected to locate point O. Radius OC has beenused to swing an arc CE from the center O. E is theintersection of arc CE with diameter AB. Chord CE isthe length of the side and is transferred to the circle byarc EF using chord CE as radius and C as center.The HEXAGON has been developed by dividingthe circumference into 6 equal parts.The OCTAGON method has been developed bycreating central angles of 90° to divide a circle into 4parts and bisecting each arc to divide the circumferenceinto 8 equal parts,AII-12

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