1. 5.3.2: Introduction Segments and angles are often described with measurements. Segments have lengths that can be measured with a ruler. Angles have measures that can be determined by a protractor. It is possible to determine the midpoint of a segment. Midpoint: point on the segment that divides it into 2 = parts. When drawing the midpoint, you can measure the length of the segment and divide the length in half. When constructing the midpoint, you cannot use a ruler, but you can use a compass and a straightedge (or patty paper and a straightedge) to determine the midpoint of the segment. This procedure is called bisecting a segment. 1 5.3.2: Bisecting Segments and Angles

2. Key Concepts, continued 2 5.3.2: Bisecting Segments and Angles Bisecting a Segment Using a Compass 1.To bisect, put the sharp point of your compass on endpoint A. Open the compass wider than half the distance of. 2.Make a large arc intersecting. 3.Without changing your compass setting, put the sharp point of the compass on endpoint B. Make a second large arc. It is important that the arcs intersect each other in two places. 4.Use your straightedge to connect the points of intersection of the arcs. 5.Label the midpoint of the segment C. Do not erase any of your markings. is congruent to.

3. Key Concepts, continued 3 5.3.2: Bisecting Segments and Angles Bisecting a Segment Using Patty Paper 1.Use a straightedge to construct on patty paper. 2.Fold the patty paper so point A meets point B. Be sure to crease the paper. 3.Unfold the patty paper. 4.Use your straightedge to mark the midpoint of. 5.Label the midpoint of the segment C. is congruent to.

4. Key Concepts, continued 4 5.3.2: Bisecting Segments and Angles Bisecting an Angle Using a Compass 1.To bisect ∠ A, put the sharp point of the compass on the vertex of the angle. 2.Draw a large arc that passes through each side of the angle. 3.Label where the arc intersects the angle as points B and C. 4.Put the sharp point of the compass on point B. Open the compass wider than half the distance from B to C. 5.Make a large arc. 6.Without changing the compass setting, put the sharp point of the compass on C. (continued)

5. Key Concepts, continued 5 7.Make a second large arc. It is important that the arcs intersect each other in two places. 8.Use your straightedge to create a ray connecting the points of intersection of the arcs with the vertex of the angle, A. 9.Label a point, D, on the ray. Do not erase any of your markings. ∠ CAD is congruent to ∠ BAD. 5.3.2: Bisecting Segments and Angles

6. Key Concepts, continued 6 5.3.2: Bisecting Segments and Angles Bisecting an Angle Using Patty Paper 1.Use a straightedge to construct ∠ A on patty paper. 2.Fold the patty paper so the sides of ∠ A line up. Be sure to crease the paper. 3.Unfold the patty paper. 4.Use your straightedge to mark the crease line with a ray. 5.Label a point, D, on the ray. ∠ CAD is congruent to ∠ BAD.

7. Common Errors/Misconceptions inappropriately changing the compass setting moving the patty paper before completing the construction not creating large enough arcs to find the point of intersection attempting to measure lengths and angles with rulers and protractors 7 5.3.2: Bisecting Segments and Angles

8. Guided Practice Example #2: Construct a segment whose measure is the length of 8 5.3.2: Bisecting Segments and Angles

9. Guided Practice: Example #2, continued 1.Copy the segment and label it. 9 5.3.2: Bisecting Segments and Angles

10. Guided Practice: Example #2, continued 10 5.3.2: Bisecting Segments and Angles

11. Guided Practice: Example 2, continued 11 5.3.2: Bisecting Segments and Angles

12. Guided Practice: Example #2, continued 12 5.3.2: Bisecting Segments and Angles is congruent to. and are both the length of.

13. Guided Practice: Example #2, continued 5.Find the midpoint of. Make a large arc intersecting. Put the sharp point of your compass on endpoint P. Open the compass wider than half the distance of Draw the arc, as shown on the next slide. 13 5.3.2: Bisecting Segments and Angles

14. Guided Practice: Example #2, continued 14 5.3.2: Bisecting Segments and Angles

15. Guided Practice: Example #2, continued 15 5.3.2: Bisecting Segments and Angles

16. Guided Practice: Example #2, continued 16 5.3.2: Bisecting Segments and Angles Do not erase any of your markings. is congruent to. is the length of. ✔

17. Guided Practice Example #4: Construct an angle whose measure is the measure of ∠ S. 17 5.3.2: Bisecting Segments and Angles

18. Guided Practice: Example #4, continued 1.Copy the angle and label the vertex S. 18 5.3.2: Bisecting Segments and Angles

19. Guided Practice: Example #4, continued 19 5.3.2: Bisecting Segments and Angles

20. Guided Practice: Example #4, continued 20 5.3.2: Bisecting Segments and Angles

21. Guided Practice: Example #4, continued 21 5.3.2: Bisecting Segments and Angles

22. Guided Practice: Example #4, continued Use your straightedge to create a ray connecting the point W with the vertex of the angle, S. 22 5.3.2: Bisecting Segments and Angles m<TSW = ½(m<TSU)

23. Guided Practice: Example #4, continued Make a large arc intersecting the sides of ∠ WSU. Put the sharp point of the compass on the vertex of ∠ S and swing the compass so that it passes through each side of ∠ WSU. Label where the arc intersects the angle as points X and Y. 23 5.3.2: Bisecting Segments and Angles

24. Guided Practice: Example #4, continued 24 5.3.2: Bisecting Segments and Angles

25. Guided Practice: Example #4, continued 25 5.3.2: Bisecting Segments and Angles

26. Guided Practice: Example #4, continued 26 5.3.2: Bisecting Segments and Angles m<TSZ = ¾(m<TSU)

27. 1) 5.3.2 Homework Workbook, P.75,76 # 1-10 (skip #3, for #4: use CD instead) 2) 5.3.3 Notes(U5-86) a)Intro: read only b)Key Concepts: copy 1 chart on P.U5-90, Constructing Parallel Lines c)?’s and summary d)Workbook: P.81 #1 27