Construct TW congruent to KM.

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Presentation transcript:

Construct TW congruent to KM. Basic Constructions LESSON 1-7 Additional Examples 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 Quick Check

Step 1: Draw a ray with endpoint Y. Basic Constructions LESSON 1-7 Additional Examples 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.

Step 4: Open the compass to the length EF. Basic Constructions LESSON 1-7 Additional Examples (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. Quick Check

Step 1: Put the compass point on point A and draw a short arc. Make Basic Constructions LESSON 1-7 Additional Examples Quick Check Use a compass opening less than AB. Explain why the construction of the perpendicular bisector of AB shown in the text is not possible. 1 2 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.

WR bisects AWB. m AWR = x and m BWR = 4x – 48. Find m AWB. Basic Constructions LESSON 1-7 Additional Examples 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 = –48 Subtract 4x from each side. x = 16 Divide each side by –3. m AWR = 16 m BWR = 4(16) – 48 = 16 Substitute 16 for x. m AWB = m AWR + m BWR Angle Addition Postulate m AWB = 16 + 16 = 32 Substitute 16 for m AWR and for m BWR.

Construct MX, the bisector of M. Basic Constructions LESSON 1-7 Additional Examples Construct MX, the bisector of M. Step 1: Put the compass point on vertex M. Draw an arc that intersects both sides of M. Label the points of intersection B and C. Step 2: Put the compass point on point B. Draw an arc in the interior of M.

Step 3: Put the compass point on point C. Basic Constructions LESSON 1-7 Additional Examples (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. Quick Check