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MATH 7-WEEK 1 PPT-BASIC CONCEPTS IN GEOMETRY.ppt
- 1. Activity 1: Array of Letters Directions: The array of letters below includes ten basic geometric terms including the two words already marked. These words are arranged horizontally, vertically, and diagonally. On a separate piece of paper, list down all the geometric terms that you can find.
- 2. Group the following phrases into three groups according to their similarities. Specify the similar characteristic per group. a dash of salt the tip of a pencil the top of a table the edge of the page of a book the tip of an umbrella the floor of the classroom the surface of the blackboard the edge of a ruler a. Which among the groups can you determine possible representations of a point? b. Which among the groups can you determine possible representations of a line? c. Which among the groups can you determine possible representations of a plane?
- 3. Ask the students to: Draw a point. Draw a line. Draw a plane
- 4. Video clip about points, lines, and planes. https://www.youtube.com/watch?v =k5etrWdIY6o
- 5. BASIC CONCEPTS IN GEOMETRY AND KINDS OF ANGLES
- 6. USING UNDEFINED TERMS AND DEFINITION A definition uses known words to describe a new word. In geometry, some words such as point, line and plane are undefined terms or not formally defined.
- 7. UNDEFINED TERMS Words that do not have formal definitions but there is an agreement about what they mean.
- 8. POINT
- 9. USING UNDEFINED TERMS AND DEFINITION •A point has no dimension. It is usually represented by a small dot. A Point A
- 10. LINE
- 11. USING UNDEFINED TERMS AND DEFINITION •A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. In this book, lines are always straight lines. A B l Line l or AB
- 12. PLANE
- 13. USING UNDEFINED TERMS AND DEFINITION A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end even though the drawing of a plane appears to have edges. A B C Plane M or plane ABC
- 14. A FEW BASIC CONCEPTS . . . • Must be commonly understood without being defined. One such concept is the idea that a point lies on a line or a plane. • Collinear points are points that lie on the same line. • Coplanar points are points that lie on the same plane.
- 15. For this section, we will be having another activity! Group the following phrases into three groups according to their similarities. Specify the similar characteristic per group. Copy and answer this activity on a separate sheet of paper.
- 17. Reflect on this: Carpentry requires an understanding of points, lines, and planes. What other line of work requires an understanding of points, lines, and planes?
- 20. Before we proceed, let us have a review about the previous lessons by answering the given activity below. Refer to the figure at the right to answer the questions that follow. 1.Name all the lines. 2. Name all the segments. 3. Name all the rays.
- 26. COLLINEAR POINTS
- 27. COPLANAR POINTS
- 28. EX. 1: NAMING COLLINEAR AND COPLANAR POINTS a. Name three points that are collinear Solution: D, E and F lie on the same line, so they are collinear. G D E H
- 29. EX. 1: NAMING COLLINEAR AND COPLANAR POINTS b. Name four points that are coplanar. Solution: D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn. G D E H
- 30. EX. 1: NAMING COLLINEAR AND COPLANAR POINTS b. Name four points that are coplanar. Solution: D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn. A B C E
- 31. EX. 1: NAMING COLLINEAR AND COPLANAR POINTS c. Name three points that are not collinear. Solution: There are many correct answers. For instance, points H, E, and G do not lie on the same line. G D E H
- 32. MORE . . . • Another undefined concept in geometry is the idea that a point on a line is between two other points on the line. You can use this idea to define other important terms in geometry. • Consider the line AB (symbolized by AB). l Line l or AB B A
- 33. MORE . . . • The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. l Line l or AB A A B B Segment AB
- 34. MORE . . . • The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie on the same side of A as point B. l Line l or AB A A B B Ray AB
- 35. MORE . . . • Note that AB is the same as BA and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions. l Line l or AB A A B B Ray BA
- 36. MORE . . . • If C is between A and B, then CA and CB are opposite rays. • Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane. l Line l or AB A C B
- 37. EX. 2: DRAWING LINES, SEGMENTS AND RAYS • Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. J K L Draw J, K and L Then draw JK
- 38. EX. 2: DRAWING LINES, SEGMENTS AND RAYS • Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. J K L Draw KL
- 39. EX. 2: DRAWING LINES, SEGMENTS AND RAYS • Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. J K L Draw LJ
- 40. EX. 3: DRAWING OPPOSITE RAYS • Draw two lines. Label points on the lines and name two pairs of opposite rays. Solution: Points M, N, and X are collinear and X is between M and N. So XM and XN are opposite rays. P M Q N X
- 41. EX. 3: DRAWING OPPOSITE RAYS • Draw two lines. Label points on the lines and name two pairs of opposite rays. Solution: Points P, Q, and X are collinear and X is between P and Q. So XP and XQ are opposite rays. P M Q N X
- 43. “Stop Dance” The students will dance as the music is running and when the music stops, the students will form an angle with the use of their body parts.
- 44. The students are ask to draw an example of an angle formed during the dance. The teacher can point out the parts of an angle using the body parts of the students. • Arms – the sides of the angle • Head – vertex of the angle
- 45. Consider the situation described below. The SPA Grade 7 students of Sapang Palay National High School will perform a dance number for their culminating activity. One of their tasks is to incorporate the arm gesture that their teacher provides to their chosen choreography. The arm gestures are as follows:
- 53. Classify whether the given measurement is acute, obtuse and right angle. 1. 100° 2. 15° 3. 90° 4. 170°
- 54. Draw the three kinds of angles according to the following given measure. Acute – 30° Right – 90° Obtuse – 100°
- 55. Follow-up Activity: 1. In a journal, write the importance of knowing the classification of an angle and give at least 2 examples of each.
- 58. Drill: Perform the following operations 1)____ + 45 = 90 2)____ + 35 = 180 3) 65 +_____ = 180 4)____- 30 = 60 5)____- 108 = 72
- 60. There are four main types of angles. Straight angle 180o Right angle 90o Acute angle Less than 90o Obtuse angle More than 90o A B C A B C A B C B A C Types Of Angles
- 61. Complementary Two angles are complementary if the sum of their measures is equal to 90 degrees. Supplementary Angles Two angles are supplementary if the sum of their measures is equal to 180 degrees.
Editor's Notes
- #3: For this section, we will be having another activity! Group the following phrases into three groups according to their similarities. Specify the similar characteristic per group. Copy and answer this activity on a separate sheet of paper.