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Basic Constructions

In Exercises 1-6, sketch each figure. 1. CD 2. GH 3. AB 4. line m 5. acute ABC 6. XY || ST 7. DE = 20. Point C is the midpoint of DE . Find CE . 8. Use a protractor to draw a 60° angle. 9. Use a protractor to draw a 120° angle. Basic Constructions. Basic Constructions.

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Basic Constructions

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  1. In Exercises 1-6, sketch each figure. 1.CD2.GH3.AB 4. line m5. acute ABC6.XY || ST 7.DE = 20. Point C is the midpoint of DE. Find CE. 8. Use a protractor to draw a 60° angle. 9. Use a protractor to draw a 120° angle. Basic Constructions

  2. Basic Constructions GEOMETRY LESSON 1-7 Solutions 1-6. Answers may vary. Samples given: 1. The figure is a segment whose endpoints are C and D. 2. The figure is a ray whose endpoint is G. 3. The figure is a line passing through points A and B. 4.5. The figure is an angle whose measure is between 0° and 90°. 6. The figure is two segments in a plane whose corresponding lines are parallel. 1-7

  3. Basic Constructions GEOMETRY LESSON 1-7 7. Since C is a midpoint, CD = CE; also, CD + CE = 20; substituting results in CE + CE = 20, or 2CE = 20, so CE = 10. 8.9. Solutions (continued) 1-7

  4. Construction vidoes • http://teachers.henrico.k12.va.us/math/igo/01Fundamentals/1_6.html

  5. Construct TW congruent to KM. Step 1: Draw a ray with endpoint T. Step 2: Open the compass to the length of KM. Step 3: With the same compass setting, put the compass point on point T. Draw an arc that intersects the ray. Label the point of intersection W. TWKM Basic Constructions GEOMETRY LESSON 1-7 1-7

  6. Step 1: Draw a ray with endpoint Y. Step 2: With the compass point on point G, draw an arc that intersects both sides of G. Label the points of intersection E and F. 75° Step 3: With the same compass setting, put the compass point on point Y. Draw an arc that intersects the ray. Label the point of intersection Z. Basic Constructions GEOMETRY LESSON 1-7 Construct Y so that YG. 1-7

  7. (continued) Step 4: Open the compass to the length EF. Keeping the same compass setting, put the compass point on Z. Draw an arc that intersects the arc you drew in Step 3. Label the point of intersection X. Step 5: Draw YX to complete Y. Y G Basic Constructions GEOMETRY LESSON 1-7 Quick Check

  8. Start with AB. Step 2: With the same compass setting, put the compass point on point B and draw a short arc. Step 1: Put the compass point on point A and draw a short arc. Make sure that the opening is less than AB. 1 2 Basic Constructions GEOMETRY LESSON 1-7 Quick Check 1 2 Use a compass opening less than AB. Explain why the construction of the perpendicular bisector of AB shown in the text is not possible. Without two points of intersection, no line can be drawn, so the perpendicular bisector cannot be drawn. -7

  9. WR bisects AWB. mAWR = x and m BWR = 4x – 48. Find mAWB. Draw and label a figure to illustrate the problem mAWR = mBWRDefinition of angle bisector x = 4x – 48Substitute x for mAWR and 4x – 48 for mBWR. m AWR = 16m BWR = 4(16) – 48 = 16 Substitute 16 for x. mAWB = m AWR + mBWRAngle Addition Postulate mAWB = 16 + 16 = 32 Substitute 16 for m AWR and for m BWR. Basic Constructions GEOMETRY LESSON 1-7 Quick Check –3x = –48 Subtract 4x from each side. x = 16 Divide each side by –3. 1-7

  10. Step 3: Put the compass point on point C. Using the same compass setting, draw an arc in the interior of M. Make sure that the arcs intersect. Label the point where the two arcs intersect X. Step 4: Draw MX. MX is the angle bisector of M. Basic Constructions GEOMETRY LESSON 1-7 (continued) 1-7

  11. Use the figure at right. NQ bisects DNB. 1. Construct AC so that ACNB. 2. Construct the perpendicular bisector of AC. 3. Construct RST so that RSTQNB. 4. Construct the bisector of RST. 5. Find x. 6. Find mDNB. Basic Constructions GEOMETRY LESSON 1-7 For problems 1-4, check students’ work. 17 88

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