Basic_Constructions ------------------------------------------

geometry

1. GEOMETRY LESSON 1-7
Basic Constructions
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.

2. 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.
GEOMETRY LESSON 1-7
Basic Constructions
Solutions
1-6. Answers may vary. Samples given:
1-7

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

4. Construction vidoes
http://teachers.henrico.k12.va.us/math/igo/01Fundamentals/1_6.html

5. Step 2: Open the compass to the length of KM.
Construct TW congruent to KM.
Step 1: Draw a ray with endpoint T.
GEOMETRY LESSON 1-7
Basic Constructions
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

6. Construct Y so that Y G.
Step 1: Draw a ray with endpoint Y.
GEOMETRY LESSON 1-7
Basic Constructions
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 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°
1-7

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

8. Start with AB.
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.
GEOMETRY LESSON 1-7
Basic Constructions
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
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
-7
Quick Check

9. –3x = –48 Subtract 4x from each side.
x = 16 Divide each side by –3.
m AWR = m BWR Definition of angle bisector
x = 4x – 48 Substitute x for m AWR and
4x – 48 for m BWR.
m AWB = m AWR + m BWRAngle Addition Postulate
m AWB = 16 + 16 = 32 Substitute 16 for m AWR and
for m BWR.
Draw and label a figure to illustrate the problem
WR bisects AWB. m AWR = x and
m BWR = 4x – 48. Find m AWB.
m AWR = 16
m BWR = 4(16) – 48 = 16 Substitute 16 for x.
GEOMETRY LESSON 1-7
Basic Constructions
1-7
Quick Check

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

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