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December 16, 2011

December 16, 2011. Grab a Computation Challenge, keep it face down and put your name on the back. Write your homework in your agenda: Review notes on constructions and continue to study vocabulary. Take out your angle pair relationship worksheet.

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December 16, 2011

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  1. December 16, 2011 • Grab a Computation Challenge, keep it face down and put your name on the back. • Write your homework in your agenda: Review notes on constructions and continue to study vocabulary. • Take out your angle pair relationship worksheet. • Sharpen your pencils. Get ready for LOTS of notes.

  2. Angle Pair Relationship • Linear pair 2) Adjacent 3) Adjacent 4) Complementary 5) Vertical 6) Adjacent 7) Linear pair 8) Vertical 9) 1300 10) 430 11) 550 12) 270 13) 1450 14) 610 15) 230 16) 1310 17) 900 18) 730 19) x = 23 20) x = 59 21) x = 20 22) x = 8

  3. What am I learning today? Constructions What will I do to show that I learned it? Perform basic constructions using both a compass and straightedge.

  4. QUESTION How do I construct line segments? http://www.mathopenref.com/constcopysegment.html

  5. Constructing Line Segments 1) Draw a line segment and label it AB A B 2) Draw a Ray PS so it’s longer than AB A B P S

  6. Constructing Line Segments 3) Draw an arc through point B on line segment AB. A B P S

  7. Constructing Line Segments 4) Keep the same setting on the compass. Draw an arc that intersects PS at a new point Q. A B P S Q

  8. QUESTION How do I construct congruent angles? http://www.mathopenref.com/constcopyangle.html

  9. Constructing Congruent Angles 1) Draw an angle and label it PQR P Q R

  10. Constructing Congruent Angles 2) Draw a Ray ST. P Q R S T

  11. Constructing Congruent Angles 3) Place the compass at vertex Q. Use a small setting on the compass. Draw an arc that intersects both sides of PQR to make points X and Y. P Q R X Y

  12. Constructing Congruent Angles 4) Keeping the same setting and place on point S. Draw an arc that intersects ST. Label the intersection Point A. X P Q Y R S A T

  13. Constructing Congruent Angles 5) Set the compass to measure the distance from point X to point Y. Keeping that setting, draw an arc that intersects the existing arc. Label that intersection Point M. P X Q Y R S A T M

  14. Constructing Congruent Angles • Draw a Ray SM. M S T

  15. QUESTION How do I bisect line segments? http://www.mathopenref.com/constbisectline.html

  16. Bisecting Line Segments • Draw a line segment CD. C D

  17. Bisecting Line Segments 2) Set the compass so that it is more than halfway to D. Draw an arc “above” and “below” CD. C D

  18. Bisecting Line Segments 3) Keeping the same setting on the compass, place the compass on point D and draw another arc “above” and another “below”. The intersections create two new points Q and R. Q C D R

  19. Bisecting Line Segments 4) Draw a line segment by connecting points Q and R. This will intersect CD at a new Point M. This is the bisector for CD. Q M C D R

  20. QUESTION How do I bisect angles? http://www.mathopenref.com/constbisectangle.html

  21. Bisecting Angles • Draw an angle and label it Angle ABC. A B C

  22. Bisecting Angles 2) Draw an arc that intersects both sides of the angle. Label the points of intersection X and Y. A X B Y C

  23. Bisecting Angles 3) Place the compass at point X and set it more than halfway to Y. Draw an arc in the interior of Angle ABC. A X B Y C

  24. Bisecting Angles 4) Keep that same setting and place the compass at point at Y. Draw an arc that intersects the arc you just drew. Label the intersection T. A X B Y C T

  25. Bisecting Angles 5) Draw a Ray BT. This is the bisector of Angle ABC. A X B Y C T

  26. December 16, 2011 • Grab a Computation Challenge, keep it face down and put your name on the back. • Write your homework in your agenda: Review notes on constructions and continue to study vocabulary. • Sharpen your pencils. Get ready for LOTS of notes.

  27. QUESTION How are parallel lines created using a compass? http://www.mathopenref.com/constparallel.html

  28. Constructing Parallel Lines 1) Draw a line and label it AB. B A

  29. Constructing Parallel Lines 2) Draw a ray at an angle with its endpoint on the line. Label a point R on the ray. R A B

  30. Constructing Parallel Lines 3) Set the compass about halfway between the endpoint of the ray and point R. Make an arc that intersects both the line and ray.

  31. Constructing Parallel Lines R A B

  32. Constructing Parallel Lines 4) Keep the same compass setting. Move the compass to point R. Draw an arc.

  33. Constructing Parallel Lines R A B

  34. Constructing Parallel Lines 5) Use the compass to measure the width of the first arc. Keep the same setting and make another arc from the intersection the upper arc and intersect it.

  35. Constructing Parallel Lines R A B

  36. Constructing Parallel Lines 6) Draw a line through point R and the intersection created by the two upper arcs.

  37. Constructing Parallel Lines R A B

  38. QUESTION How are perpendicular lines created using a point on the line? http://www.mathopenref.com/constperplinepoint.html

  39. Constructing Perpendicular Lines with a Point on the Line 1) Draw a line. Label a point A on the line. A

  40. Constructing Perpendicular Lines 2) From point A on the line, draw an arc to the right and the left of point A. A

  41. Constructing Perpendicular Lines 3) Set the compass on the left intersection and extend it between point A and right intersection. Draw an arc above the line.

  42. Constructing Perpendicular Lines A

  43. Constructing Perpendicular Lines 4) Keeping the same setting, do the same from the right intersection. 5) Draw a line through point A and the intersection of the two arcs.

  44. Constructing Perpendicular Lines A

  45. QUESTION How are perpendicular lines created using a point in space?

  46. Constructing Perpendicular Lines with a Point in Space 1) Draw a line AB. Label a point X in space above the line. X A B

  47. Constructing Perpendicular Lines 2) Draw an arc from point X that crosses line AB in two places. Label these points D and E. X D E A B

  48. Constructing Perpendicular Lines 3) Set the compass on point D and extend it more than halfway to point E. Draw an arc below the line. X D E A B

  49. Constructing Perpendicular Lines 4) Keeping the same compass setting, set the compass on point E. Draw another arc below the line that intersects the first arc. X D E A B

  50. Constructing Perpendicular Lines 5) Draw a line through point X and the intersections of the two arcs. X E D B A

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