Parallelism and perpendicularity

Grade 8 Discussion on Parallelism and Perpendicularity

1. Parallelism and Perpendicularity

2. Math Prayer Lord, You have created us in different shapes and angles But still you made sure that we are congruent one way or another. No matter which sides, even if there are terms undefined, your teachings will remain our guide. May our lesson today maybe made parallel with what you want us to become. And by the time our paths perpendicularly crossed, may we face you with confidence That you will shower us with your unending love and providence. AMEN.

3. This lesson seeks to answer the question: “ How can we establish parallelism or perpendicularity of lines? ”

4. Activity 1: Optical Illusion Can you see straight lines in the picture? ________ Do these lines meet/intersect? ________ Are these lines parallel? Why? ________ Are the segments on the faces of the prism below parallel? Why? ________

5. Activity 1: Optical Illusion What can you say about the edges of the prism? ________ Describe the edges that intersect and the edges that do not intersect. ________

6. Activity 2: Agree or Disagree . Read each statement under the TOPIC column and write A if you agree with the statement; otherwise, write D . Before-Lesson Response TOPIC: Parallelism and Perpendicularity 1. Lines on the same plane that do not intersect are parallel lines. 2. Skew lines are coplanar. 3. Transversal is a line that intersects two or more lines. 4. Perpendicular lines are intersecting lines. 5. If two lines are parallel to a third line, then the two lines are parallel. 6. If two lines are perpendicular to the same line, then the two lines are parallel. 7. If one side of a quadrilateral is congruent to its opposite side, then the quadrilateral is a parallelogram. 8. Diagonals of a parallelogram bisect each other. 9. Diagonals of a parallelogram are congruent. 10. Diagonals of a parallelogram are perpendicular.

7. Discussion: Parallelism 1. Two lines are parallel if and only if they are coplanar and they do not intersect . 2. A line that intersects two or more lines is called a transversal. a. The angles formed by the transversal with the two other lines are called: Exterior Angles ( Interior Angles (   b. T he pairs of angles formed by the transversal with the other lines are called: Corresponding Angles {Congruent} Alternate Interior Angles ( {Congruent} Alternate Exterior Angles ( {Congruent} Interior Angles on the Same Side of the Transversal ( {Supplementary} Exterior Angles on the Same Side of the Transversal (  

8. For Example: If is 37 therefore, is 37 Vertical Angles 2 is 143 Linear Pair 4 is 143 Linear Pair 5 is 37 Alternate Interior Angles 6 is 143 Supplementary Angles 7 is 37 Corresponding Angles 8 is 143 Supplementary Angles  

9. Activity 3: Name it: Complete the table below using the given figure as your reference: Given that the angle number 6 is equal to 71.04◦, find the other angles. (Hint: 180.00 will be used instead of 180) 1 & 5, 2&6, 3&7, 4&8 3&6, 4&5 1&8, 2&7 3&5, 4&6 1&7, 2&8

10. Discussion: Perpendicularity Two lines that intersect to form right angles are said to be perpendicular . Line segments and rays can also be perpendicular. A perpendicular bisector of a line segment is a line or a ray or another line segment that is perpendicular to the line segment and intersects it at its midpoint. The distance between two parallel lines is the perpendicular distance between one of the lines and any point on the other line. Perpendicular distance between parallel lines

11. Get ready!

12. A. Identify the following: Corresponding Angles __________________________________________________ Alternate Interior Angles ________________________________________________ Alternate Exterior Angles _____________________ Interior Angles on the Same Side of the Transversal _____________________ Exterior Angles on the Same Side of the Transversal __________________________ B. Solve for the following: If angle 1 = 120, find the measurement of the other angles.

13. A. Identify the following: Corresponding Angles 1 and 5, 2 and 6, 3 and 7, 4 and 8 Alternate Interior Angles 4 and 5, 3 and 6 Alternate Exterior Angles 1 and 8, 2 and 7 Interior Angles on the Same Side of the Transversal 4 and 6, 3 and 5 Exterior Angles on the Same Side of the Transversal 1 and 7, 2 and 8 B. Solve for the following: If angle 1 = 120 Given 5 = 120 (Corresponding/Supplementary) 2 = 60 (Supplementary/Alternate exterior/corresponding) 6 = 60 (Supplementary) 3 = 60 (Vertical Angle/Supplementary) 7 = 60 (Vertical Angle/Supplementary 4 = 1 20 (Vertical Angle/Supplementary) 8 = 120 Vertical Angle/Supplementary

14. Review on Parallel lines Using the figure in Individual Work A p. 301 of your book, Identify the following (for 65 points). Write your answers in your notebook 2 sets of corresponding angles 2 sets of alternate interior angles 2 sets of alternate exterior angles 2 sets of interior side of the transversal 2 sets of exterior side of the transversal B. Solve: If <10 = 20º find angles 1,2,3,4,9,11, and 12 If < 13 = 17.01º find angles 5,6,7,8,14,15 and 16

15. Given 1 and 3 Definition of Parallel lines