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**Basic Constructions In Exercises 1-6, sketch each figure.**

GEOMETRY LESSON 1-7 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. In Exercises 1-6, sketch each figure.

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**Basic Constructions Solutions 1-6. Answers may vary. Samples given:**

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. 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

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**Basic Constructions Solutions (continued)**

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. Solutions (continued) 1-7

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Construction vidoes

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**Basic Constructions Construct TW congruent to KM.**

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

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**Basic Constructions Construct Y so that Y G.**

GEOMETRY LESSON 1-7 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. 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. 1-7

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**Basic Constructions Step 4: Open the compass to the length EF.**

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

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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. Start with AB. 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 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. -7

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**Basic Constructions WR bisects AWB. m AWR = x and**

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

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**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 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

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**Basic Constructions Use the figure at right. NQ bisects DNB.**

GEOMETRY LESSON 1-7 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. For problems 1-4, check students’ work. 17 88

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Warm-up Solve the following problems for x. 1.13 + 3x – 5 = 2x 2.5x – 3 = 2x + 9 3.14 + 2x – 7 = 4x - 3.

Warm-up Solve the following problems for x. 1.13 + 3x – 5 = 2x 2.5x – 3 = 2x + 9 3.14 + 2x – 7 = 4x - 3.

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