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angle-pairs-involving-supplementary-complementary-congruent-and-vertical-angles.pptx
- 1. CONTENT STANDARDS The learner demonstratesunderstanding of the key concepts of geometry of shapes and sizes, and geometric relationships
- 2. PERFORMANCE STANDARDS The learner isable to model plane figures, formulate and solve accurately authentic problems involving sides and angles of a polygon
- 3. LEARNING COMPETENCIES Derives relationships ofgeometric figures using measurements and by inductive reasoning; supplementary angles, complementary angles, congruent angles, vertical angles, adjacent angles, linear pairs, perpendicular lines, and parallel lines. M7GE-lllb-1
- 4. CONTENT Supplementary angles, Complementary angles, Congruentangles, and Vertical angles
- 5. PRELIMINARY ACTIVITIES •PRAYER •GREETINGS •CHECKING OFATTENDANCE •SETTING OF STANDARDS
- 6. REVIEWING PREVIOUS LESSON Can anyonetell me what the topic is all about and what you have learned from it?
- 7. REVIEWING PREVIOUS LESSON WHAT ISAN ANGLE?
- 8. REVIEWING PREVIOUS LESSON An angleis formed by a two noncollinear rays with a common endpoint where two rays are called the sides of the angle and their common endpoint is called the vertex.
- 9. REVIEWING PREVIOUS LESSON A rayis subset of a line that has an endpoint and extends endlessly in one direction.
- 10.
- 11. REVIEWING PREVIOUS LESSON WHAT ARETHE THREE KINDS OF ANGLES?
- 12. REVIEWING PREVIOUS LESSON A rightangle is an angle that measures 90° while an obtuse angle is an angle that measures more than 90° but less than 180° and lastly, an acute angle is an angle that measures less than 90°.
- 13. OBJECTIVES At the endof the lesson proper, the students are expected to: 1. identify the different kinds of angle pairs involving supplementary angle, complementary angle, congruent angle and vertical angles 2. construct the different angle pairs involving supplementary angles, complementary angles, vertical angles and congruent angles with a given measurements, and; 3. solve the measurement of an undefined value of angle pairs involving supplementary angles, complementary angles, vertical angles and congruent angles.
- 14. DESCRIBE ME! The classwill be divided into 4 groups, each group will be given a paper bag containing the materials that you will use to complete the task for 2 minutes. All you need to do is to answer the given questions based on the illustration.
- 15. CRITERIA Cooperation/Teamwork – 30points Discipline – 30 points Neatness/Organize – 20 points Time Management – 20 points
- 17.
- 18. PRESENTING EXAMPLES Supplementary angles, Complementaryangles, Vertical angles and Congruent angles.
- 20. DISCUSSION Supplementary angles, Complementary angles,Vertical angles and Congruent angles.
- 21. COMPLEMENTARY ANGLE - aretwo angles whose measures have a sum of 90°.
- 24. Find the measureof the complement of angle whose measure is 40°.
- 26. SUPPLEMENTARY ANGLE - aretwo angles whose measures have a sum of 180°.
- 28. Example:The measure ofthe supplement of an angle is 30° more than 4 times the measure of an angle. Find the measure of each angle. To solve the problem, we need to let x as the measure of the angle and y as the measure of its supplement of an angle, so; 180 – x = 4x + 30; where 180 is the sum of a supplementary angle
- 29. -x – 4x= 30 – 180 -5x = -150 = x = 30
- 30. 180 – 30= 150 y = 150
- 31. 30 + 150= 180
- 32. VERTICAL ANGLES - aretwo nonadjacent angles (two angles that do not share a common vertex or side) formed by two intersecting lines. That’s why its angles are congruent to each other.
- 34. Find the measuresof all vertical angles in the figure where m 1 = 2x + 15 ∠ and m 2 = 85 – 5x ∠ Since, m∠1 and m∠2 are vertical angles, ∠1 ∠2.
- 35. m 1 =m 2 ∠ ∠ 2x + 15 = 85 – 5x 2x + 15 = 85 – 5x (combine like terms) 2x + 5x = 85 – 15 7x = 70 (divide both sides by 7) x = 10
- 36. 2(10) + 15= 85 – 5(10) 20 + 15 = 85 -50 35 = 35, therefore the m 1 is ∠ congruent to m 2 since its ∠ angles are both 35°.
- 37. 180° - 35°= 145° Since, the measure of ∠1 and ∠2 is congruent and based from the definition of a vertical angles, its angles are congruent to each other so, the measure of ∠3 is congruent to ∠4. Therefore, m∠3 and m∠4 is 145°.
- 38. CONGRUENT ANGLES - twoangles are congruent if their measures are equal.
- 41. CONSTRUCT AND SOLVEIT! The class will be divided into 8 groups.All you need to do is to construct and solve each angle pairs involving supplementary angles, complementary angles, vertical angles and congruent angles within a time limit of 5 minutes.You will write it in a 1 whole sheet of paper.
- 42. FOR GROUP 1AND GROUP 5 Find the measure of the complementary angle with a given angle of 26°. Construct the angles.
- 43. FOR GROUP 2AND GROUP 6 Find the measure of the supplementary angle with a given angle of 45°. Construct the angles.
- 44. FOR GROUP 3AND GROUP 7 Two angles are vertical angles. If one angle measures 5y+3 and the other angle measures 2y + 15, find the measures of each angle. Construct the angles.
- 45. FOR GROUP 4AND GROUP 8 Find the measure of ABC of a ∠ congruent angle if JKE ∠ measures 75°. Construct the angles.
- 47. FINDING PRACTICAL APPLICATION How canwe relate those four angle pairs in real life?
- 48. For example, weare going to measure the angle of a pie in which it is divided into 8 pieces and if we take 2 pieces of the pie. If one of the pies has a measure of 45° and the other is 135°, what is the total measurement of both pie?
- 49. What angle pairis being formed when the colors are orange to blue- violet? How about when the colors are yellow-orange to yellow-green? What is the congruent of the colors blue-green to yellow-orange? What is the congruent vertical angle when the colors blue to green is a vertical angle?
- 50. GENERALIZING Who can tellme in their own understanding, what is a Supplementary angle? How about a Complementary angle? Vertical angles? And Congruent angles? Yes, ______?
- 51. GENERALIZING When can wesay that an angle is a supplementary? Complementary angle? Vertical angles? Congruent angles?
- 52. GENERALIZING How can wesolve the measurement of the different angle pairs?
- 53. Instructions: You willwrite your answers in a ¼ sheet of paper and there will be 10 questions. Instructions: For questions 1-4, identify the angle pairs being described.
- 54. 1. It isan angle pair where two angles whose sum of their measures is 90°. 2. It is an angle pair where two angles whose sum is 180°. 3. It is a pair of non-adjacent angles formed by the intersection of two straight lines where the opposite angles are both congruent 4. It is two angles that have the same measurement.
- 55. For questions 5– 8, use the given figure to answer the following questions.
- 56. 5.What is theangle that is supplementary to ABD? ∠ 6. If m ABD = 160°, what is m CBD? ∠ ∠
- 57. 7. What isthe angle that is complementary to ∠CBF? 8. Based from the given illustration, give the congruent angles.
- 58. 9-10. Based fromthe illustration of a pyramid, if m GFH ∠ is 135°, then what is the measure of m EFG? Hint. ∠ m EFH is a ∠ supplementary angle.
- 59. Before ending ourmeeting, are there any clarifications or questions among any of you?
Editor's Notes
- #6 Before I proceed to the new topic, I would like to know first if all of you can still remember the previous topic that you have tackled together with your teacher. Can anyone tell me what the topic is all about and what you have learned from it?
- #8 What is a ray?
- #9 What is a ray?
- #10 who can write the symbol of a ray given the illustration? Since, you already know the symbol of a ray, when can we say that the side of the angle is a ray?
- #11 The three kinds of angles are right, obtuse and acute angles. If these three are the kinds of angles, when can we say that an angle is a right angle, obtuse angle and acute angles?
- #12 Very good! Let’s give your classmates a round of applause. It seems like all of you have already proven to understand the previous topic, are you all ready to listen and participate in the journey of our new lesson?
- #13 So, can I expect all of you to identify, construct and solve angle pairs involving those four angles? If so, are you all ready to play a game?
- #14 Before we proceed to the game, I will be scoring the activities you will be doing for the rest of the discussion.
- #15 Is the mechanics of the game clear? How about for the scoring? Do you have any questions? If none, then let’s proceed to the game. Are you all ready? Okay, 2 minutes starts now.
- #17 Now that you have done the activity so well. What do you think will be our topic this morning? Before I start discussing to you the lesson, let me first give you real life examples so that when I introduce to you the topic later on, you can relate to it and understand the lesson easily.
- #18 Based on the activity that you did a while ago, there are four angle pairs which are supplementary angles, complementary angles, vertical angles and congruent angles. If you look at the illustration of those angles, in what real life object can we relate those angle pairs?
- #19 That’s right! We can relate those angle pairs in a scissors, pyramids, clothes hanger, clock, etc Another example where we can relate angle pairs in a real-life setting is when we compare the angle of the corner of the ceiling to the other corner. Based from the given example, what angle pairs can you identify? Very good! Later on, I will be discussing why this object relates to the lesson that we will tackle today.
- #20 As you can see from the previous activity we have conducted, we will discuss about angle pairs. In geometry, relationship exist between two angles. These relationships can be used as basis for classifying angle pairs. The angle pairs include adjacent angles, complementary angles, supplementary angles, linear pairs, vertical angles and congruent angles. However, I will only discuss supplementary angles, complementary angles, congruent angles and vertical angles today and the rest will be discussed tomorrow.
- #22 Based from the given example, the complementary angles in this illustration are ∠SOI and ∠IOL because the m∠SOI which is 60° + m∠IOL which is 30° equals to 90° and according to the definition of a complementary angle, it has a sum of 90°.
- #23 One example of complementary angle in real life is a wall clock where the time is exactly 3 o’clock. Another example is when we cut a pizza into 2 slices and we ate those 2 slices of pizza, what is the angle formed from the eaten pizza?
- #25 Do you have any questions about the process in measuring the complement of an angle? If none, I will now proceed to supplementary angles. Everyone, please read the definition.
- #27 Based on the given example, ∠MAD and ∠DAE are supplementary angles since the sum of 135° and 45° is equal to 180°. According to the definition of a supplementary angle, the measure of the two angles is equal to 180°. Therefore, this illustration is a supplementary angle. To measure a supplement of an angle with only one given degree, let’s consider this example;
- #28 In solving the equation, we need to apply the addition property of equality wherein we need to transpose the 4x to the left side and 180 to the right side. So, it will be like this;
- #29 In this part, we need to apply the multiplication property of equality where we need to find the number that can eliminate the -5 to the left side for it to be only x. What is the number that can eliminate -5? Then, we need to substitute the value of x to the equation 180 – x to get the measure of the supplement of the angle. So,
- #30 To check if the answer is correct, we need to get the sum of the measure of the angle and the measure of its supplement of an angle so,
- #31 Therefore, the angle measures 30° and it’s supplement measures 150°. Do you have any questions regarding supplementary angles? If none, then please read the definition of a vertical angles.
- #35 To check if the value of x is correct, substitute it to the equation.
- #36 To find the measure of ∠3 and ∠4, subtract the value of 35° to 180° so,
- #37 Do you have any questions about vertical angles? If none, then let’s proceed. Everybody, read the definition of a congruent angles.
- #39 Based from the given example, ∠CAB ∠EDF (∠CAB is congruent to ∠EDF) since they have the same measurement of angles. We can also write it as “the measure of ∠CAB is equal to the measure of ∠EDF” or m∠CAB m∠EDF. Another example:
- #40 Do have any questions about the lesson?
- #45 Are you all ready? If so, let’s start.
- #47 During the discussions and the first activity that we have done, what have you observe? How can we relate those four angle pairs in real life?
- #48 And what angle pair results in 180°? The total measurement of both pies is 180° and since a supplementary angle has a measurement of 180° then the angle pair is a supplementary angle. Who can give me other examples of how we can apply angle pairs in our daily lives? Another example is, when we apply the concept of color wheel in angle pairs, we can easily distinguish the angles based from the colors
- #49 Supplementary Angle Complementary Angle Red-Orange to blue-violet Red to Orange When can we say that an angle pair can be apply in real life situation? Well, done! It’s very true that we can apply these geometric concepts to solve mathematical and real-life problems. It seems that you have a lot of ideas for its applications. Why do you think it’s necessary for us to learn these concepts? Yes, _____? Very good analyzation ______! Yes, learning these concepts are necessary for us in order to make sense of the things around us.
- #50 Now that we are finished with discussing the relevance of linear equation in our lives, let us see if you have truly understood the lesson. Put your right hand up if you want to answer the question.
- #52 Very good! I can see that you have a good grasp of the lesson and have demonstrated a clear understanding of the relationships between them.
- #53 To evaluate your learning, I will give you a short test about angle pairs.
- #59 If there is none, then that concludes today’s lesson. Thank you for your participation and goodbye everyone!