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GEOMETRY LESSON 1-7 Basic Constructions 1. CD2. GH3. AB 4. line m5. 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. In Exercises 1-6, sketch each figure.

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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 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. GEOMETRY LESSON 1-7 Basic Constructions Solutions 1-6. Answers may vary. Samples given: 1-7

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

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Construction vidoes

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Step 2: Open the compass to the length of KM. Construct TW congruent to KM. Step 1: Draw a ray with endpoint T. GEOMETRY LESSON 1-7 Basic Constructions 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. TW KM 1-7

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Construct Y so that Y G. Step 1: Draw a ray with endpoint Y. GEOMETRY LESSON 1-7 Basic Constructions 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. 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° 1-7

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(continued) GEOMETRY LESSON 1-7 Basic Constructions Y G Step 5: Draw YX to complete Y. 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. Quick Check

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

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

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Step 4: Draw MX. MX is the angle bisector of M. (continued) 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. GEOMETRY LESSON 1-7 Basic Constructions 1-7

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For problems 1-4, check students work NQ bisects DNB. 1. Construct AC so that AC NB. 2. Construct the perpendicular bisector of AC. 3. Construct RST so that RST QNB. 4. Construct the bisector of RST. 5. Find x. 6. Find m DNB. Use the figure at right. GEOMETRY LESSON 1-7 Basic Constructions

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