1 5 Basic Constructions Copying A Segment Step

1 -5: Basic Constructions

Copying A Segment

Step #1: • Start with the original segment

Step #2: • Using a straightedge, draw a line that is longer than the original segment

Step #3: • Place the needle of the compass on point A and the pencil on point B

Step #4: • Transfer the distance to the drawn line, making an arc

Step #5: • Label the new points A’ and B’. Then erase the excess line.

Bisecting a Segment

Step #1: • Place the needle of the compass on point B and the pencil on a point about 3/4 across the segment

• Make a semi-circle

Step #2: • Maintaining the same distance on your compass, repeat step #1 from point A

Step #3: • Label the points of intersection of the semi-circles points C and D

Step #4: • Using a straightedge connect points C and D

• is the perpendicular bisector of

Copying an Angle

Step #1: • Using a straightedge, draw a line segment that is about the same length as the base ray of the original angle

Step #2: • Placing the needle of the compass on the vertex of the original angle and the pencil at a point located on the base ray

Step #3: • Construct an arc

Step #4: • Maintaining the same distance on your compass, place the needle of the compass on vertex of the new angle and construct an arc

Step #5: • Placing the needle of your compass on the lower point of intersection of the arc and the pencil on the other point of intersection, measure the distance on the original angle

• make an arc

Step #6: • Maintaining the same distance on your compass, place the needle of the compass on the point on the new angle where the arc and the base ray intersect

• make a small arc that intersects the first constructed arc

Step #7: • Using a straightedge, draw a line that starts at the vertex of the new angle and passes through the point where the two arcs intersect

Bisecting an Angle

Step #1: • Starting with the given angle…

…place the needle of the compass on the vertex and the pencil on some point on the base ray…

…make an arc

Step #2: • Placing the needle of the compass on a point where the arc and one of the rays of the angle intersect, construct an arc in the interior of the angle

Step #3: • Repeat step #2 starting at the other point where the arc and a ray intersect

Step #4: • Label the point where the two arcs intersect point B…

…and using a straightedge draw a ray from A through B

is the angle bisector of

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 HELP KM Quick Check GEOMETRY

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. HELP GEOMETRY

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. Step 5: Draw YX to complete Y Y. G Quick Check HELP GEOMETRY

Basic Constructions LESSON 1 -7 Additional Examples Quick Check 1 Use a compass opening less than 2 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 1 AB. 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. HELP GEOMETRY

Basic Constructions LESSON 1 -7 Additional Examples Quick Check m WR bisects AWB. m AWR = x and BWR = 4 x – 48. Find m AWB. Draw and label a figure to illustrate the problem m m HELP 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 AWR = 16 Substitute 16 for x. BWR = 4(16) – 48 = 16 AWB = m AWR + m BWR Angle Addition Postulate AWB = 16 + 16 = 32 Substitute 16 for m AWR and for m BWR. GEOMETRY

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. HELP GEOMETRY

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 HELP GEOMETRY