1. Copyright © Ed2Net Learning, Inc.1 Perpendicular, parallel & intersecting lines Grade 4

2. Copyright © Ed2Net Learning, Inc.2 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

3. Copyright © Ed2Net Learning, Inc. 3 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.

4. Copyright © Ed2Net Learning, Inc. 4 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

5. Copyright © Ed2Net Learning, Inc. 5 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

6. Copyright © Ed2Net Learning, Inc. 6 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

7. Copyright © Ed2Net Learning, Inc. 7 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.

8. Copyright © Ed2Net Learning, Inc. 8  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

9. Copyright © Ed2Net Learning, Inc. 9 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)

10. Copyright © Ed2Net Learning, Inc. 10 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

11. Copyright © Ed2Net Learning, Inc. 11 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

12. Copyright © Ed2Net Learning, Inc. 12 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

13. Copyright © Ed2Net Learning, Inc. 13 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

14. Copyright © Ed2Net Learning, Inc. 14 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

15. Copyright © Ed2Net Learning, Inc. 15 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.

16. Copyright © Ed2Net Learning, Inc. 16 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

17. Copyright © Ed2Net Learning, Inc. 17 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:

18. Copyright © Ed2Net Learning, Inc. 18 BREAK

19. Copyright © Ed2Net Learning, Inc. 19

20. Copyright © Ed2Net Learning, Inc. 20 Assignments Classify each pair of lines as parallel, intersecting, or perpendicular. 4 12 3

21. Copyright © Ed2Net Learning, Inc. 21 Classify each pair of lines as parallel, intersecting, or perpendicular. 8 56 7

22. Copyright © Ed2Net Learning, Inc. 22 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

23. Copyright © Ed2Net Learning, Inc. 23 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

24. Copyright © Ed2Net Learning, Inc. 24 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

25. Copyright © Ed2Net Learning, Inc. 25 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.

26. Copyright © Ed2Net Learning, Inc. 26 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

27. Copyright © Ed2Net Learning, Inc. 27 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:

28. Copyright © Ed2Net Learning, Inc. 28 You have done a nice job. Remember to do the practice worksheets!!!