Geometric Designs PDF

GEOMETRIC DESIGNS OBJECTIVES: › Develop profound appreciation for the beauty and significance of geometric designs in various context › Analyze and interpret geometric basics › Appreciate inher...

GEOMETRIC DESIGNS OBJECTIVES: › Develop profound appreciation for the beauty and significance of geometric designs in various context › Analyze and interpret geometric basics › Appreciate inherent geometry found in nature and its creative application in artistic expression GEOMETRIC BASICS.N POINT. -indicates position or M location -it has no dimension but can be. represented by a dot A -it is named by using a capital letter  GEOMETRIC BASICS LINE.. -is an infinitely long and A B. E F C l straight set of points -it has no thickness nor width -it is named by using any two points on the line or one small letter BF or FB - Represented by GEOMETRIC BASICS LINE SEGMENT.. - A path between two B F points - Denoted by naming its end BF or FB GEOMETRIC BASICS RAY. - Has only one point B F and extends indefinitely in one direction from that point BF GEOMETRIC BASICS PLANE - Is an infinitely wide and flat set of points - It has no thickness - It has 2 dimensions - It represented by GEOMETRIC BASICS POSTULATE 1 POSTULATE A line, a plane and space each contain an - Is statement infinite number of points that is accepted as POSTULATE 2 true without For any two points, there is exactly one line proof containing them POSTULATE 3 For any three noncollinear points, there is exactly one plane containing them GEOMETRIC BASICS POSTULATE 4 POSTULATE If two points are on a plane, then the line - Is statement containing them lie on the plane that is accepted as POSTULATE 5 true without Two lines intersect in one and only one proof point POSTULATE 6 Two planes intersect in one and only one line GEOMETRIC BASICS POSTULATE 7 POSTULATE Corresponding to every pair of distinct - Is statement points, there is one and only one positive real number called the distance between that is them accepted as true without proof POSTULATE 8 IF A, B and C are collinear and B is... between A and C , then AB + BC = AC A B C  M N A B s 0 1 2 3 4 5 6 7 8 9 10 GEOMETRIC BASICS BISECTOR and MIDPOINTS OF LINE SEGMENT m.. - If three points such as A, P, and B are collinear and if P is A P B between A and B such that AP = PB, then P is the midpoint of AB - If line m and AB intersect at P , we say that m bisects AB and call m the bisector of AB ANGLE and ANGLE RELATIONS  B ANGLE - is the union of two rays that have a A common end point C - The rays are called the sides of the angle - The common end point is called the vertex of an angle EQUAL ANGLE - are angles that have the same measure BISECTOR OF AN ANGLE - is a ray in the interior of the angle that divides the angle into two equal angles VERTICAL ANGLES - are opposite angle formed by two intersecting lines COMPLEMENTARY ANGLES - are two angles whose sum is 90 degree SUPPLEMENTARY ANGLES - are two angles whose sum is 180 degree LINES and TRANSVERSALS GEOMETRIC BASICS PARALLEL LINES INTERSECTING LINES - Lines that are coplanar - Lines that are coplanar and do not intersect and share exactly one point GEOMETRIC BASICS SKEW LINES TRANSVERSAL - Two lines that do not - Line that intersects two or intersect and are not in the more coplanar lines at same plane different points GEOMETRIC BASICS PERPENDICULAR LINES - When two lines (rays or segments) meet to form right angles TRIANGLES GEOMETRIC BASICS TRIANGLE - Union of three noncollinear points, called vertices of the triangle, and three line segments called sides of the triangle, each segment joining a pair of these points - Formed when three noncollinear point joint by segments  NOTE: PROBLEM: In any triangle: 1. The sum of the The measure of the lengths of any two sides is greater than three angles of a the length of the third side triangle are in the ratio 2. The sum of the measures of the 2:4:9. find the angles is 180 degrees measure of each angle.  The measure of the three angles of a triangle are in NOTE: the ratio 2:4:9. find the measure of each angle. Solution: In any triangle: Let 2x be the measure of the first angle 4x be the measure of the second angle 1. The sum of the 9x be the measure of the third angle lengths of any two sides is greater than Since the sum of the measures of the three angles of a the length of the triangle is 180° then, third side 2x + 4x + 9x = 180 2. The sum of the 15 x = 180 measures of the x = 12 angles is 180 degrees Therefore : 2x = 24° (first angle) 4x = 48° (second angle) 9x = 108° ( third angle) TYPES OF TRAINGLE POLYGONS and CIRCLE  GEOMETRIC BASICS POLYGON - Is a closed figure formed by joining segments (sides of the polygon) at their end points (vertices of the polygon) - We named the polygon according to the number of sides they have  GEOMETRIC BASICS - A polygon is regular if all sides are congruent and all its angles are congruent  GEOMETRIC BASICS QUADRILATERALS - a polygon having four sides, four angles, and four vertices - derived from the Latin words 'quadri,' which means four, and 'latus', which means side PERIMETER - The sum of all the lengths of the sides of a polygon AREA - the number of unit squares that cover the surface of a closed figure GEOMETRIC BASICS CIRCLE - a shape consisting of all points in a plane that are at a given distance from a given point, the center  Tangent Chord Radius Diameter Secant -line that the distance or -a straight the distance length of the a line touches from the circle at one line that line segment that center of the from one end point. connects circle to any of the circle to intersects -At the point two points point on it's the other end a circle at of Tangency, on the circumferen of the circle two Tangent to a ce passing circumfer through the distinct circle is ence of a center of the points always circle perpendicula circle r to the radius.