Mathematics - GEOMETRY and its basic concepts.pptx
- 1. Teacher Shahanie A, Dulnuan
- 2. - A branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids - Derived from Ancient Greek words – ‘Geo’ means ‘Earth’ and ‘metron’ means ‘measurement’
- 3. - Euclid was a Greek mathematician who was also called Euclid of Alexandria, the founder of geometry - Born on 330 B.C. - His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry). - Father of GEOMETRY.
- 4. 1. Construction of Buildings 2. Computer Graphics 3. Art 4. Measuring Orbits and Planetary Motions 5. Interior Design Uses of Geometry
- 6. Geometry •The ancient Egyptians, Chinese, Babylonians, Romans, and Greeks used geometry for surveying, navigation, astronomy, and other practical occupations.
- 7. 1. Two-dimensional shapes 2. Three-dimensional shapes
- 8. Plane Geometry deals with flat shapes which can be drawn on a piece of paper. These include lines, circles & triangles of two dimensions. Plane geometry is also known as two-dimensional geometry. All the two-dimensional figures have only two measures such as length and breadth. It does not deal with the depth of the shapes. Some examples of plane figures are square, triangle, rectangle, circle, and so on.
- 9. BASIC CONCEPTS AND TERMS IN GEOMETRY GEOMETRY Mathematic s
- 10. GEOMETRY •A branch of mathematics that studies the sizes, shapes, position, angles, dimensions of things and the knowledge dealing with spatial relationship. •This is from the Ancient Greek words: “geo” which means “earth” and “-metrein” which means “to measure”. The basic knowledge and concepts will help us appreciate better the beauty of nature and the things around us.
- 12. A. UNDEFINED TERMS POINT LINE PLANE
- 13. POINT A point is the simplest figure. It is represented by a dot. It has no dimensions , no length, no width, no height , no thickness and occupies no space. All geometric figures are made up of points. It is usually designated by a capital letter like A, B, C or D, and it could be found in a line, a plane or in a space ( the set of all points ). ●P
- 14. LINE A series of points that extends in opposite directions without end. One-dimensional length. No width or thickness. It can be determined by using two points. Has an arrowhead on each end representing the fact that it goes on forever. A B Line AB or AB Line BA or BA Line m or m m Can be called
- 15. PLANE A flat surface that extends forever in two dimensions (has length & width). Contains infinitely many points and lines. Usually represented by a four-sided figure. Named with a capital script letter or 3 points on the surface of the plane A B C W Can be named: Plane W Plane ABC Plane BCA Plane CBA, etc.
- 16. 6. The electrical wire 7. The tip of a needle 8. The intersection of walls 9. The 4 corners of the ceiling 10. The edge of a straight road Exercises 1. Getting to know each other ! Tell whether each of the following represents a point, line or a plane. 1. A grain of salt 2. A cheeseboard 3. A piece of paper 4. The top of a table 5. The window pane Point Plane Plane Plane Plane Line Point Line Point Line
- 17. ACTIVITY Draw figures using point, lines, and shapes
- 18. ACTIVITY Draw figures using point, lines, and shapes
- 19. 1. COLLINEAR ARE POINTS THAT LIE ON THE SAME LINE. More definitions on Undefined Concepts MORE DEFINITIONS B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES
- 20. 2. COPLANAR ARE POINTS THAT LIE ON THE SAME PLANE. MORE DEFINITIONS B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts
- 21. 3. INTERSECTING LINES Two or more lines are intersecting if they have a common point. MORE DEFINITIONS B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts
- 22. 4. PARALLEL LINES These are coplanar lines that do not meet. MORE DEFINITIONS B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts
- 23. 5. CONCURRENT LINES Three or more lines are concurrent if they all intersect at only one point MORE DEFINITIONS B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts
- 24. 6. SKEW LINES These are lines that do not lie on the same plane. MORE DEFINITIONS B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINES More definitions on Undefined Concepts
- 25. Slide Title 3 4 6 7 9 10 11 12 5 8 PLANE
- 26. DRAW FIGURES/OBJECTS USING THE BASIC CONCEPT OF GEOMETRY
- 32. Exercises 3. Who I am? Recognize the following as a point, a line , or a plane. 1. An exact location 2. These are contained in same line 3. These are contained in same plane 4. These are lines that do not lie on the same plane. 5. Three or more lines are concurrent if they all intersect at only one point 6. The power button of a remote control 7. A figure that goes infinitely in both directions 8. These are lines that do not meet. 9. Two or more lines are intersecting in a common point. 10. A flat surface that extends forever in two dimensions (has length & width). Point Collinear Coplanar SKEW Concurrent Point Line Parallel Intersecting Plane
- 33. Exercises 5.Let’s Make a Figure ! Draw and label the following. 1. a line m 2. a point N 3. a plane B 4. a point lying on line l 5. line BC lying on plane A 6. a point E lying on plane Y 7. two points MN lying on a line MN 8. line b intersects planes M and N 9. a plane D intersecting a line k at point J 10. a point O lying in the intersection of lines r and s
- 34. c. Subsets of a Line See definition of Line
- 35. c. Subsets of a Line
- 36. •If the line to which a line segment belongs is given a scale so that it turns into the real line, then the length of the segment can be determined by getting the distance between end points.
- 37. •Given the points on the number line below, the length of the following segments may be derived. 1. AB = |(−6) – (−3)| = 3 UNITS 2.CD = | 0 – (3)| = 3 UNITS 3.BD = | (−3) – (3)| = 6 UNITS 4.BC = |(−3) – (0)| = 3 UNITS 5.AC = |(−6) – (0)| = 6 UNITS •Segments are congruent if they have the same length. So, AB and CD, BC and CD, and AC and BD are pairs of congruent segments.
- 38. •The points A, B, C are on ray AC. However, referring to another ray BC, the point A is not on ray BC. The points of AB are all the points on segment AB such that B is between A and C. •If JM is extended in the direction of point J, a line is formed. Point C is the common endpoint of the two rays. •CJ and CM are opposite rays.
- 39. Identify the geometric term described in each sentence. Choose the terms from the list below. ________________ 1. IT IS A SUBSET OF A LINE WITH ONE ENDPOINT AND AN ARROWHEAD. ________________ 2. POINTS OR LINES THAT DO NOT LIE ON THE SAME PLANE. ________________ 3. IT HAS NO DIMENSION. ________________ 4. TWO OR MORE COPLANAR LINES THAT MEET AT A COMMON POINT. ________________ 5. IT IS A FLAT SURFACE. ________________ 6. THREE OR MORE LINES THAT INTERSECT AT ONLY ONE POINT. ________________ 7. THESE ARE LINES THAT WILL NEVER MEET. ________________ 8.IT IS A SET OF POINTS EXTENDED INFINITELY IN BOTH DIRECTIONS. ________________ 9. IT IS A SUBSET OF A LINE WITH TWO ENDPOINTS. ________________ 10. POINTS OR LINES THAT LIE ON THE SAME PLANE. QUIZ # 1: A. IDENTIFICATION
- 40. CHOICES:
- 41. 1. Which of the following has no dimention? a.Line b. Line Segment c. Point d. Ray 2. Which of the following geometric term which have length but no width and height? a. Line b. Line segment c. Point d. Ray 3. What is a ray? a. A ray is a small segment b. A ray starts at an endpoint and extends to infinity c. A ray starts at an endpoint and ends at an endpoint d. A ray is infinite line 4. What are endpoints? a. They are all the points that make up a segment b. They are points that indicate a beginning or ending position c. They are all the points that make up a line d. They are endless points QUIZ #1 B. Multiple Choice: Choose the best answer.
- 42. 5. What is a line ? a. A set of points that go on forever in opposite directions b. A set of points between two endpoints c. A set of points that begin at one point and extend to infinity in one direction d. A set of points that goes on round and round 6. How is a line different from a ray? a. A line goes on forever in two opposite directions while a ray has one endpoint and on forever in one direction b. A line goes on forever in two opposite directions while a ray has two endpoints c. A line and a ray are the same thing d. A line goes on one direction while a ray goes on opposite directions QUIZ #1 B. Multiple Choice: Choose the best answer.
- 43. 7. What is the difference between a line and a line segment? a. lines are finite b. lines segments are measurable ,lines are immesurable c. lines are measurable, line segments are immeasurable d. lines is a subset of line segments ,line segment is a subset of a ray 8. What do line segments and rays have in common? a. both goes on both directions b. both begin at an endpoint c. both are measurable d. both have two endpoints 9. What geometric term that both ends go on infinity? a. point b. Lines c. Plane d. Ray QUIZ #1 B. Multiple Choice: Choose the best answer.
- 44. 10. Which of the following statements is FALSE? a. It’s possible to have a line segment inside a ray b. It’s possible to have a ray inside the line c. It’s possible to have a line segment inside a line d. It’s possible to have a line in a line segment QUIZ #1 B. Multiple Choice: Choose the best answer.
- 45. Activity 2 : NAME ME Direction: Use the figure to name each of the following.
- 46. Activity 3 : Use the figure to answer each question
- 47. Activity 3 : Use the figure to answer each question
- 48. ANGLES
- 49. Basics of Geometry Rays are important because they help us define something very important in geometry…Angles! An angle consists of two different rays that have the same initial point. The rays are sides of the angles. The initial point is called the vertex. Angles vertex sides A B C Notation: We denote an angle with three points and symbol. The middle point is always the vertex. We can also name the angle with just the vertex point. This angle can be denoted as: A or CAB, , BAC Types of angles
- 50. Basics of Geometry Angles vertex sides A B C A or CAB, , BAC Types of angles 45° 95°
- 51. Basics of Geometry Angles vertex sides A B C A or CAB, , BAC Types of angles 100° 180°
- 52. Basics of Geometry Angles vertex sides A B C A or CAB, , BAC Types of angles 1° 250°
- 53. Basics of Geometry Angles vertex sides A B C A or CAB, , BAC Types of angles 0° 360°
- 54. Basics of Geometry Angles vertex sides A B C A or CAB, , BAC Types of angles 211° 120°
- 55. Basics of Geometry Rays are important because they help us define something very important in geometry…Angles! An angle consists of two different rays that have the same initial point. The rays are sides of the angles. The initial point is called the vertex. Angles vertex sides A B C Notation: We denote an angle with three points and symbol. The middle point is always the vertex. We can also name the angle with just the vertex point. This angle can be denoted as: A or CAB, , BAC Types of angles
- 56. ANGLE RELATIONSHIPS Geometry is a branch of mathematics that deals with questions of shape, size, relative position of figures, and the properties of space. It is practically dealing with lengths, areas, and volumes. Fundamental concepts in geometry includes point, line, plane, distance, angle, surface, and curve.
- 60. Activity 1: Find the value of x in the set of supplementa ry angles
Editor's Notes
- #2: Objectives Define Geometry
- #4: 5 Uses Geometry in our Daily Life 1. Construction of Buildings The best use of geometry in daily life is the construction of buildings, dams, rivers, roads, temples, etc. For ages, geometry has been exceptionally used to make temples that hold the heritage of our country. Some of these famous temples are even counted as miraculous developments done by people with primitive instruments. 2. Computer Graphics The audiovisual presentation in different segments such as education, entertainment, etc uses geometry as a part of the art and creativity. Computer graphics is a prime application of geometry in day-to-day life we can consider here. Smartphones, laptops, computers, etc are designed using geometrical concepts. The games we play also use geometry to find relevance between the distance and shapes of objects designed. 3. Art Another excellent use of geometry is how artists use the concepts to design the best paintings and express their ideologies. The use of colours, brushes, and different strokes give birth to excellent artwork. Artists also design apparel, accessories, and other items we use. You can understand the importance of geometry in daily life. 4. Measuring Orbits and Planetary Motions This concept is used by astronomers to track stars, measure the orbits and distance between planets and satellites. Scientists also measure the factors and set the path of satellites launched. This is one of the best applications of coordinate geometry in daily life. 5. Interior Design The applications of coordinate geometry in daily life can also be found in interior design. Setting new items in an open space is done perfectly using the concepts of coordinate geometry.
- #5: Illustrate the importance of Geometry in real life
- #7: In Euclidean geometry, there are two-dimensional shapes and three-dimensional shapes 3. Define Two-dimentional shapes
- #8: In Euclidean geometry, there are two-dimensional shapes and three-dimensional shapes
- #9: 4. Define the Basic concept and terms in Geometry
- #11: Rearrange the highlighted letters to form the word described.
- #12: In Euclidean Geometry, the geometric terms point, line, and plane are all undefined terms and are purely mental concepts or ideas. However, we can use concrete objects around us to represent these ideas. Thus, these undefined terms can only be described.
- #17: 5. Draw figures using point, lines, and shapes
- #18: 5. Draw figures using point, lines, and shapes
- #25: DIFFERENT KINDS OF PLANE IN GEOMETRY
- #26: Use the basic concepts in Geometry in real life
- #27: Use the basic concepts in Geometry in real life
- #28: Use the basic concepts in Geometry in real life
- #29: Use the basic concepts in Geometry in real life
- #30: Use the basic concepts in Geometry in real life
- #31: Exercises 2. 1. AB and AD, AD and CD, CD and CB, CB and AB 2. ABC and CDA 3. AC 4. A 5. ABCD
- #32: Exercises 3.Who I Am ? 1. Point 6. Point 2. Collinear 7. Line 3. Coplanar 8. Line 4. Segment 9. Ray 5. Point 10. Plane
- #41: C A B B
- #42: 5. A 6. A
- #43: 7. B 8. B 9.
- #44: 10. D
- #60: ANSWER KEY Activity 1 135° 60° 90° 30° 80° 95° 151° 71° 5° 170°
- #61: ANSWER KEY Activity 2 28° 4° 82° 63° 19° 88° 77° 1° 45° 71°
- #62: ANSWER KEY Activity 3 Vertical angles Adjacent angles Linear pair Congruent angles Adjacent angles Vertical angles Adjacent angles Linear pair Congruent angles Adjacent angles