2. Sketching Intersections Section 1.4

3. Objective Sketch simple figures and their intersections.

4. Key Vocabulary Intersect Intersection

5. Postulates Postulate 3: Intersection of Two Lines Postulate 4: Intersection of Two Planes

6. Definitions Intersect – When geometric figures have any points in common. Intersection – Is the point or points that two or more geometric figures have in common.

7. Intersection of Lines The intersection of two lines is a point. m n P Line m and line n intersect at point P.

8. Intersection of Lines Two lines can intersect even if a diagram does not show where they intersect. The lines above intersect at a point that is not shown. m n

9. Intersection of a Lines and a Planes 3 Possibilities of Intersection of a Line and a Plane. (1) Line passes through plane – intersection is a point. (2) Line lies on the plane - intersection is a line. (3) Line is parallel to the plane - no common points.

10. Intersection of Two Planes P R A B Plane P and Plane R intersect at the line The intersection of two planes is a line.

11. Postulates Postulate 3: Intersection of Two Points  If two lines intersect, then their intersection is a point. Postulate 4: Intersection of Two Planes  If two planes intersect, then their intersection is a line. s t P P is the point of intersection. P R d d is the line of intersection.

12. b.Name the intersection of BE and DF. a.Name the intersection of AC and BE. Use the diagram at the right. c.Name the intersection of AC and DF. SOLUTION a.AC and BE intersect at point B. b. BE and DF intersect at point E. c.AC and DF do not appear to intersect. Example 1:

13. SOLUTION a.Planes S and R intersect at line k. b.Planes R and T do not appear to intersect. c.Planes T and S intersect at line l. a.Name the intersection of planes S and R. c.Name the intersection of planes T and S. Use the diagram at the right. b.Name the intersection of planes R and T. Example 2:

14. ANSWER point R ANSWER point U ANSWER They do not appear to intersect. Use the diagram at the right. 1.Name the intersection of PS and QR. 2.Name the intersection of TV and QU. 3.Name the intersection of PS and UV. Your Turn:

15. Use the diagram at the right. ANSWER line p 1.Name the intersection of planes X and Y. 2.Name the intersection of planes Y and Z. 3.Name the intersection of planes Z and X. ANSWER line q ANSWER They do not appear to intersect. Your Turn:

16. Sketching Intersections Sketch a line that intersects a plane in one point  Draw a plane and a line.  Emphasize the point where they meet.  Dashes indicate where the line is hidden by the plane

17. Sketching Intersections Sketch two planes that intersect in a line.  Draw two planes.  Emphasize the line where they meet.  Dashes indicate where one plane is hidden by the other plane.

18. Sketch a plane. Then sketch each of the following. a.a line that is in the plane b.a line that does not intersect the plane c.a line that intersects the plane at a point SOLUTION a.Draw the plane. Then draw a line in the plane. Example 3:

19. b.Draw the plane. Then draw a line above or below the plane. c.Draw the plane. Then draw a line that intersects the plane. Example 3:

20. Sketch two planes that intersect in a line. SOLUTION 1.Draw one plane as if you are looking straight at it. Shade the plane. 2.Draw a second plane that is horizontal. Shade this plane a different color. 3.Draw the line of intersection. Use dashed lines to show where one plane is hidden. Your Turn:

21. 1.Sketch three lines that lie in a plane. 2.Sketch two lines that intersect a plane at the same point. 3.Sketch two planes that do not intersect. ANSWER Your Turn:

22. Joke Time Which sea creature can add up? An octoplus! What did the confused bee say? To bee or not to bee!

23. Assignment Section 1-4, pg. 25-27: #1 – 31 odd, 35 – 39 odd