Basic Constructions GEOMETRY LESSON 1 7 In Exercises

Basic Constructions GEOMETRY LESSON 1 -7 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 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

Basic Constructions GEOMETRY LESSON 1 -7 Solutions (continued) 7. Since C is a midpoint, CD = CE; also, CD + CE = 20; substituting results in CE + CE = 20, or 2 CE = 20, so CE = 10. 8. 9. 1 -7

Construction vidoes l http: //teachers. henrico. k 12. va. us/math/igo/01 Fundamentals/1_6. html

Basic Constructions GEOMETRY LESSON 1 -7 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. TW KM 1 -7

GEOMETRY LESSON 1 -7 Basic Constructions Construct Y so that Y G. 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. 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. 1 -7 75°

GEOMETRY LESSON 1 -7 Basic Constructions (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 Quick Check

GEOMETRY LESSON 1 -7 Basic Constructions Quick Check 1 Use a compass opening less than AB. Explain why the 2 construction of the perpendicular bisector of AB shown in the text is not possible. 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 1 sure that the opening is less than AB. 2 Without two points of intersection, no line can be drawn, so the perpendicular bisector cannot be drawn. -7

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

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

GEOMETRY LESSON 1 -7 Basic Constructions Use the figure at right. NQ bisects DNB. For problems 1 -4, check students’ work. 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. 17 6. Find m DNB. 88