1. CONFIDENTIAL1 Good Afternoon! Today we will be learning about Perpendicular, parallel & intersecting lines Let’s warm up : 1) Name a line segment with R as an end point. 2) Name a ray with R as an end point. 3) Name a ray with S as an end point. 4) Name two line segments with S as an end point. R Q S T 1) SR 2) RQ 3) ST 4) SR, ST

2. CONFIDENTIAL 2 Let’s review what we did in the last session Geometry is all about shapes and their properties. The two most common subjects in geometry are: 1) Plane Geometry 2) Solid Geometry Plane geometry: is the study of plane figures in the plane such as points, lines, line segments, rays, angles, circles, triangles, quadrilaterals, and other polygons... shapes that can be drawn on a piece of paper. Solid Geometry: is the study of three dimensional objects like cubes and pyramids. It is called three- dimensional, or 3D because there are three dimensions: width, depth and height.

3. CONFIDENTIAL 3 Review Point  A point is an exact location.  Points are dimensionless, i.e., a point has no width, length, or height. We locate points relative to some arbitrary standard point, often called the "origin". A point is a location in space. X

4. CONFIDENTIAL 4 Review A line is a group of points on a straight path that extends to infinity. Any two points on the line can be used to name it. This line is called line DE.  Its length, having no limit, is infinite.  It has no width or height. D E DE Line

5. CONFIDENTIAL 5 Review A line segment is a part of a line that has two end points. A line segment is the path of shortest distance between two points. The two end points of the line segment are used to name the line segment. This line segment is called segment XY. All the points "between" the two points make up a line segment. A line segment has one dimension, length. It has no width or height. XY XY Line segment

6. CONFIDENTIAL 6 Review A ray is part of a line. A ray extends indefinitely in one direction, but ends at a single point in the other direction. That point is called the end-point of the ray. Ray A ray is named starting with its end point first and then any other point on the ray second. OP OP This ray is called ray OP.

7. CONFIDENTIAL 7  A line has no end-points. NOTE:  A line segment has two end-points.  A ray one end-point. A D B C O Using the graphic in the figure we see that: A, B, C, D and O are points. DB is a line. AC, OC, and AC are line segments. OD and OB are rays. Review

8. CONFIDENTIAL 8 Review 654321654321 1 2 3 4 5 6 X- scale Y- scale Draw a line segment between points (1,5) and (5,5) on the XY-scale. STEP1: Mark the points (1,5) and (5,5) on the XY-scale. X X point (1,5) point (5,5)

9. CONFIDENTIAL 9 Review STEP2: Join the points (1,5) and (5,5) on the XY-scale.. 654321654321 1 2 3 4 5 6 X X Y- scale X- scale

10. CONFIDENTIAL 10 Let’s start with Perpendicular, parallel & intersecting lines For any two lines in the same plane, one of two relationships can occur: The lines will run parallel to each other, They will intersect. OR

11. CONFIDENTIAL 11 Parallel lines Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. They will travel to infinity in either direction and never intersect. Lines m and l are parallel lines. l m

12. CONFIDENTIAL 12 Intersecting lines Lines can only intersect at one point and only one point. x y Two or more lines that meet at a point are called intersecting lines. That point would be on each of these lines. In the Figure, lines x and y are intersecting lines and intersect at point Q. Q

13. CONFIDENTIAL 13 s t If the line segments meet or cross each other to form square corners, they are perpendicular to each other. Perpendicular lines. The little box drawn in the corner, means "at right angles“. right angles

14. CONFIDENTIAL 14 In other words, when two lines intersect and form right angles (90°), they are called perpendicular lines. Lines s and t are perpendicular lines. Perpendicular lines. Perpendicular lines intersect at a point and form 4 right angles. s t Perpendicular lines form 4 square corners.

15. CONFIDENTIAL 15 What is the difference between perpendicular and parallel? 90 degrees (a right angle) If you rotate a perpendicular line by 90° it will become parallel (but not if it touches!), and the other way around. perpendicular lines rotate parallel

16. CONFIDENTIAL 16 SymbolMeaningExampleIn Words || parallel EF||GH The line EF is parallel to line GH perpendi cular AB CD The line AB is perpendicular to line CD Right angle is 90° A right angle is 90 degrees Symbols in Geometry Here are the some geometrical symbols:

17. CONFIDENTIAL 17 BREAK

18. CONFIDENTIAL 18 GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/kids- jigsaw-puzzles/12-piece-jigsaw/11-16-06-merry.html

19. CONFIDENTIAL 19 Assignments Classify each pair of lines as parallel, intersecting, or perpendicular. 4 12 3 1) Parallel 2) Intersecting 3) Perpendicular 4) Parallel

20. CONFIDENTIAL 20 Classify each pair of lines as parallel, intersecting, or perpendicular. 8 56 7 5) Perpendicular 8) Perpendicular7) Parallel 6) Intersecting

21. CONFIDENTIAL 21 Very Good! Let's Review For any two lines in the same plane, one of two relationships can occur: The lines will run parallel to each other, They will intersect. OR

22. CONFIDENTIAL 22 Review Parallel lines Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. They will travel to infinity in either direction and never intersect. Lines m and l are parallel lines. l m

23. CONFIDENTIAL 23 Review Intersecting lines Lines can only intersect at one point and only one point. x y Two or more lines that meet at a point are called intersecting lines. That point would be on each of these lines. In the Figure, lines x and y are intersecting lines and intersect at point Q. Q

24. CONFIDENTIAL 24 Review s t If the line segments meet or cross each other to form square corners, they are perpendicular to each other. Perpendicular lines. The little box drawn in the corner, means "at right angles“. right angles Perpendicular lines intersect at a point and form 4 right angles.

25. CONFIDENTIAL 25 Review What is the difference between perpendicular and parallel? 90 degrees (a right angle) If you rotate a perpendicular line by 90° it will become parallel (but not if it touches!), and the other way around. perpendicular lines rotate parallel

26. CONFIDENTIAL 26 Review SymbolMeaningExampleIn Words || parallel EF||GH The line EF is parallel to line GH perpendi cular AB CD The line AB is perpendicular to line CD Right angle is 90° A right angle is 90 degrees Symbols in Geometry Here are the some geometrical symbols:

27. CONFIDENTIAL 27 You have done a nice job. See you in the next session.