<p>UNIT 2: GEOMETRIC SHAPES</p><p>A SHAPE is a 2-dimensional area that is defined in some way. It could be by a line, space, color, texture or a variety of other ways. There are two types of shapes: geometric and free-form (organic)</p><p>A GEOMETRIC SHAPE is a shape that follows a mathematical rule.</p><p>These are the most important ones: POLYGONS</p><p>DEFINITION: A polygon is a shape closed by straight lines</p><p>REGULAR polygons are those which have EQUAL SIDES AND ANGLES TRIANGLES</p><p>QUADRILATERALS REGULAR POLYGONS INSCRIBED IN A CIRCUMFERENCE</p><p>Definition: They are the regular polygons that have all their vertices (the plural of vertex is vertices) </p><p>ON the circumference (not inside the circle) In this unit we will learn how to make:</p><p>1. An EQUILATERAL TRIANGLE INSCRIBED IN A CIRCUMFERENCE 2. AN ISOSCELES TRIANGLE INSCRIBED IN A CIRCUMFERENCE (THIS IS NOT REGULAR) 3. A SQUARE INSCRIBED IN A CIRCUMFERENCE 4. A PENTAGON INSCRIBED IN A CIRCUMFERENCE 5. A HEXAGON INSCRIBED IN A CIRCUMFERENCE 6. A HEPTAGON INSCRIBED IN A CIRCUMFERENCE 7. AN OCTAGON INSCRIBED IN A CIRCUMFERENCE 1.- EQUILATERAL TRIANGLE. INSCRIBED IN A CIRCUMFERENCE</p><p> st 1 Draw a circumference centered in o</p><p> nd 2 Draw any diameter AP .</p><p> rd 3 Draw an arch centered in O and with OP radius until it cuts the circumference in B and C.</p><p>4st Link the vertices A, B and C.</p><p>2.- AN ISOSCELES TRIANGLE INSCRIBED IN A CIRCUMFERENCE (THIS IS NOT REGULAR) If when drawing the arch you do not pass through the center you will obtain an isosceles triangle 3.- A SQUARE INSCRIBED IN A CIRCUMFERENCE st 1 Draw a circumference centered in O</p><p> nd 2 Draw any diameter AP .</p><p> rd 3 Draw its perpendicular bisector</p><p>A</p><p>C O D</p><p> th 4 Link the vertices A, C, B and D. B</p><p>4.- A PENTAGON INSCRIBED IN A CIRCUMFERENCE</p><p>ST 1 Follow the steps 1 2 and 3 as to make a square </p><p>A</p><p>C O D</p><p> nd 2 Draw the bisector of OD (you will obtain M)</p><p>A B</p><p>B</p><p>C O M D nd 3 Draw an arch centered in M with MA radius, from A till you reach CO (you will obtain L)</p><p>A</p><p>A</p><p>C O M D th L 4 Transferring the measure AL through the circumference we will obtain the vertices of the pentagon.</p><p>C O M D L</p><p>B</p><p>B 5.- A HEXAGON INSCRIBED IN A CIRCUMFERENCE </p><p> st 1 Draw two arches with the same radius than the circumference (OB) centered in A and in B until they cut the circumference.</p><p>You will obtain D, C, E and F</p><p>2º Link A, E, D, B, C and F.</p><p>6.- A HEPTAGON INSCRIBED IN A CIRCUMFERENCE Following the GENERAL METHOD</p><p>Following the GENERAL METHOD METHOD for how TO DRAW ANY REGULAR POLYGON (INSCRIBED IN A</p><p>CIRCUMFERENCE) (WITH ANY NUMBER OF SIDES)</p><p>This is a general method and has a small error, so if you know the specific method for the polygon, this will be more accurate.</p><p>1º Draw any diameter (AB) A</p><p>B 2º Divide this diameter into the number of equal parts you want to obtain in the polygon; I want to get the heptagon, (7 sided polygon) so I divide the diameter into 7 equal parts. We will do this by applying the Thales theorem. </p><p>A</p><p>B</p><p> rd 3 Trace two arcs centred in each side of the diameter, and with the diameter as the radius (of the arcs). Where these two arcs intersect we will obtain the point </p><p>A</p><p>P</p><p>4th Trace a straight line starting at P till the SECOND MARK OF THE DIAMETER (NOT THE AUXILIARY LINE) and</p><p>B continue it until it reaches the circumference. We will obtain point L. </p><p>A L</p><p>P</p><p>5th The segment AL, will be the measure we have to mark consecutivelyA through the circumference to obtain the vertexes of the L polygon. B P</p><p>B 6º By joining these points with straight lines you will get the polygon (the heptagon in this particular case)</p><p>A L</p><p>P</p><p>B</p><p>7. - AN OCTAGON INSCRIBED IN A CIRCUMFERENCE ST 1 Follow the steps 1st and 2nd two draw a square</p><p>A</p><p>C O D nd 2 Then draw the bisectors of the 4 right angles. That way we obtain E, F, G y H.</p><p>B</p><p> th 3 Join the points A, E,C,G,B,F,D and H. </p>