Presentation on theme: "Basic Constructions In Exercises 1-6, sketch each figure."— Presentation transcript:
1 Basic Constructions In Exercises 1-6, sketch each figure. GEOMETRY LESSON 1-71. CD 2. GH 3. AB4. line m 5. acute ABC 6. XY || ST7. 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.
2 Basic Constructions Solutions 1-6. Answers may vary. Samples given: GEOMETRY LESSON 1-7Solutions1-6. 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.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 Solutions (continued) GEOMETRY LESSON 1-77. Since C is a midpoint, CD = CE; also, CD + CE = 20; substituting results in CE + CE = 20, or 2CE = 20, so CE = 10.Solutions (continued)1-7
5 Basic Constructions Construct TW congruent to KM. GEOMETRY LESSON 1-7Construct 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 compasspoint on point T. Draw an arc that intersects theray. Label the point of intersection W.TW KM1-7
6 Basic Constructions Construct Y so that Y G. GEOMETRY LESSON 1-7Construct 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.75°Step 3: With the same compass setting, putthe compass point on point Y. Draw an arcthat intersects the ray. Label the point ofintersection Z.1-7
7 Basic Constructions Step 4: Open the compass to the length EF. GEOMETRY LESSON 1-7Quick Check(continued)Step 4: Open the compass to the length EF.Keeping the same compass setting, put thecompass point on Z. Draw an arc that intersectsthe arc you drew in Step 3. Label the point ofintersection X.Y GStep 5: Draw YX to complete Y.
8 Basic ConstructionsGEOMETRY LESSON 1-7Quick Check12Use a compass opening less than AB. Explain why the construction of the perpendicular bisector of AB shown in the text is not possible.Start with AB.Step 1: Put the compass point onpoint A and draw a short arc. Makesure that the opening is less than AB.12Step 2: With the same compass setting,put the compass point on point B anddraw a short arc.Without two points of intersection, no line can be drawn, so the perpendicular bisector cannot be drawn.-7
9 Basic Constructions WR bisects AWB. m AWR = x and GEOMETRY LESSON 1-7Quick CheckWR bisects AWB. m AWR = x andm BWR = 4x – 48. Find m AWB.Draw and label a figure to illustrate the problemm AWR = m BWR Definition of angle bisectorx = 4x – 48 Substitute x for m AWR and4x – 48 for m BWR.–3x = – Subtract 4x from each side.x = Divide each side by –3.m AWR = m BWR = 4(16) – 48 = 16Substitute 16 for x.m AWB = m AWR + m BWR Angle Addition Postulatem AWB = = 32 Substitute 16 for m AWR andfor m BWR.1-7
10 Basic Constructions Step 3: Put the compass point on point C. GEOMETRY LESSON 1-7(continued)Step 3: Put the compass point on point C.Using the same compass setting, draw anarc in the interior of M. Make sure thatthe arcs intersect. Label the point wherethe two arcs intersect X.Step 4: Draw MX. MX is the angle bisectorof M.1-7
11 Basic Constructions Use the figure at right. NQ bisects DNB. GEOMETRY LESSON 1-7NQ 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.For problems 1-4, check students’ work.1788