Geometry: geometric figures

1. Geometry: geometric figures By Joanna Muñoz

2. Basic Geometric figures • Point (.)- A point is a location. In a figure, a point is represented by a dot and a capital letter. It has no dimensions. • Line ( )- A line is made of points and has no thickness or width. Lines are usually named by lower case or by writing capital letters for two points on the line. It has one dimension. • Segment ( )- A measurable part of a line that consists of two points, called end points, and all of the points between them.

3. Basic geometric figures • Ray ( )- Part of a line that begins in a certain point and has no end. PQ is a ray if it is the set of points consisting of PQ an all points S for which Q is between P and S. • Angle ( )- The intersection of two non collinear rays at a common end point. The rays are called sides and the common end point is called the vertex.

4. Classifying angles We use a protractor to measure angles. This tool gives us the measure in degrees, but angles can also be measured in radians. E F D C B A

5. Classifying angles • Degree (°)- is one 360th () of a full circle. The degree is further divided in to 60 minutes. For even finer measurements the minute is divided again into 60 seconds, However this last measure is so small, it only used where angles are subtended over extreme distances such as astronomical measurements, and measuring latitude and longitude. These minutes and seconds have (confusingly) nothing to do with time. They are just smaller and smaller parts of a degree.

6. Classifying angles • Radians- One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle. 1radian= 57.295… degrees

7. Classifying angles • Acute angle- An angle with a degree measure less than 90.

8. Classifying angles • Right angle- An angle with a degree measure of 90. • Obtuse angle- An angle of degree measure greater than 90 and less than 180. • Straight angle- An angle of a degree measure degree of 180.

9. Basic Geometric figures • Plane- flat surface made of points that has no depth and extends indefinitely in all directions. A plane is determined by 3 non-collinear points. It has two dimensions (2D). Collinear- points that lie on the same line.

10. polygons • Polygon- A closed figure formed by a finite number of coplanar segments called sides such that the following conditions are met: • The sides that have a common endpoint are non collinear. • Each side intersect exactly two other sides, but only at the end points. Coplanar- points that lie in the same plane.

11. polygons • Regular polygon- A convex polygon in which all of the sides are congruent and all of the angles are congruent. • Irregular figure- A polygon with sides and angles that are not all congruent.

12. polygons Concave polygon- A polygon for which there is a line containing a side of the polygon that also contains a point in the interior of the polygon. Convex polygon- A polygon for which there is no line that contains both sides of the polygon and a point in the interior of the polygon.

13. convex polygons Triangles Quadrilaterals N-gons Polygons that have 3 sides Polygons with 4 sides. Gons- mean sides The letter N is substituted by a word that means a number, for example: Pentagon- 5 sides Hexagon- 6 sides Heptagon-7 sides and so on.

14. Triangles • Sides • Scalene triangle- triangle with unequal sides. • Isosceles triangle- triangle with two equal sides. • Equilateral triangle- triangle with equal sides. • Angles • Equiangular triangle- a triangle which has all interior angles equal (congruent). • Acute triangle- triangle in which all angles are acute. • Right triangle- triangle with one right angle. • Obtuse triangle- triangle with one obtuse angle.

15. triangles

16. quadrilaterals • Trapezoid- • A quadrilateral with exactly one pair of parallel sides. The non parallel sides are called legs. Parallel sides are called bases. base legs base

17. Quadrilaterals • Parallelogram- A quadrilateral with parallels opposites sides. Any side of the parallelogram may be called base. If a parallelogram has all his angles with a measure of 90 degrees, is called rectangle. If a parallelogram has all four sides with the same measure, is called rhombus. The only figure that has the same characteristics of a rectangle, but also the rhombus is the square.

18. quadrilaterals trapezoid parallelogram Rhombus rectangle square

19. Circle • The locus of all points in a plane equidistant from a given point called the center of the circle.

20. polyhedrons • Closed three-dimensional figures made up of flat polygonal regions. The flat regions formed by the polygons and their interiors are called faces. Pairs of faces intersect in segments called edges. Points where threes or more edges intersect are called vertices.

21. polyhedrons • Parts of the polyhedron vertices edges face

22. prisms • A prism is a polyhedron that has: • Two faces, called bases, that are formed by congruent polygons that lies in parallel planes. • The faces that are not bases, called lateral faces, are formed by parallelograms. • The intersection of two adjacent lateral faces are called lateral edges and are parallel segments.

23. pyramids vertex • Polyhedron with the following characteristics: • All the faces, except one face, intersect at a point called vertex. • The face that does not contain the vertex is called the base and is a polygonal region. • The faces meeting at the vertex are called lateral faces and are triangular regions. Triangular lateral face base

24. Solids of revolution • Solid of revolution is a figure generated by revolving a line or curve (the generator) around a fixed axis. Revolve-

25. sphere In space, the set of all points that are a given distance from a given point, called the center. It is generated by rotation of semicircle around its diameter. Semicircle- an arc that measures 180 degrees. Diameter- In a circle, is a chord that passes to the center of the circle. In a sphere, is a segment that contains the center of the sphere, and has endpoints that are on the sphere.

26. cone vertex A solid with a circular base, a vertex not contained in the same plane as the base, and a lateral surface area composed of all points in the segments connecting the vertex to the edge of the base. It is generated by the rotation of a right triangle around one of its legs as the axis of revolution. base

27. cylinder A figure with bases that are formed by congruent circles in parallel planes. It is generated by rotation a rectangle by one of its sides as the axis of revolution.