1. Warm Up
1. Find CD. 8
2. Find the coordinate of the midpoint of CD. –2

2. Chapter 1.6 Construction
Learning Target: I can make basic constructions using a straightedge and a compass

3. LT: I can make basic constructions using a straightedge and a compass
Definitions
Construction – Use a straight edge and a compass to make geometric figures
Straightedge – is a ruler with no marking on it
Compass – Geometric tool used to draw circles and parts of circles called arcs
Perpendicular Lines-two lines that intersect to form right angles.
Perpendicular bisector-of a segment is a line that is perpendicular to the midpoint
LT: I can make basic constructions using a straightedge and a compass

4. LT: I can make basic constructions using a straightedge and a compass
Congruent segment
LT: I can make basic constructions using a straightedge and a compass

5. LT: I can make basic constructions using a straightedge and a compass
Congruent Angles
LT: I can make basic constructions using a straightedge and a compass

6. Perpendicular Bisector
LT: I can make basic constructions using a straightedge and a compass

7. LT: I can make basic constructions using a straightedge and a compass
Angle Bisector
LT: I can make basic constructions using a straightedge and a compass

8. Construct a triangle given three line segments
LT: I can make basic constructions using a straightedge and a compass

9. LT: I can make basic constructions using a straightedge and a compass
Assignment
Homework: P. 46 #1,2,5-16
Challenge #17 and #18 (a point each)
LT: I can make basic constructions using a straightedge and a compass

10. LT: I can make basic constructions using a straightedge and a compass
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
LT: I can make basic constructions using a straightedge and a compass

11. LT: I can make basic constructions using a straightedge and a compass
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.
LT: I can make basic constructions using a straightedge and a compass

12. LT: I can make basic constructions using a straightedge and a compass
(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.
LT: I can make basic constructions using a straightedge and a compass

13. LT: I can make basic constructions using a straightedge and a compass
Prove by construction why you cannot construct a perpendicular bisector with a compass opening less than AB. 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.
LT: I can make basic constructions using a straightedge and a compass

14. LT: I can make basic constructions using a straightedge and a compass
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.
LT: I can make basic constructions using a straightedge and a compass

15. LT: I can make basic constructions using a straightedge and a compass
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.
LT: I can make basic constructions using a straightedge and a compass

16. LT: I can make basic constructions using a straightedge and a compass
(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.
LT: I can make basic constructions using a straightedge and a compass

17. LT: I can make basic constructions using a straightedge and a compass
You can make a sketch or measure and draw a segment. These may not be exact. A construction is a way of creating a figure that is more precise. One way to make a geometric construction is to use a compass and straightedge.
LT: I can make basic constructions using a straightedge and a compass

18. LT: I can make basic constructions using a straightedge and a compass
Example 2: Copying a Segment
Sketch, draw, and construct a segment congruent to MN.
Step 1 Estimate and sketch. Estimate the length of MN and sketch PQ approximately the same length. P Q
LT: I can make basic constructions using a straightedge and a compass

19. LT: I can make basic constructions using a straightedge and a compass
Example 2 Continued
Sketch, draw, and construct a segment congruent to MN.
Step 2 Measure and draw. Use a ruler to measure MN. MN appears to be 3.5 in. Use a ruler to draw XY to have length in. X Y
LT: I can make basic constructions using a straightedge and a compass

20. LT: I can make basic constructions using a straightedge and a compass
Example 2 Continued
Sketch, draw, and construct a segment congruent to MN.
Step 3 Construct and compare. Use a compass and straightedge to construct ST congruent to MN.
A ruler shows that PQ and XY are approximately the same length as MN, but ST is precisely the same length.
LT: I can make basic constructions using a straightedge and a compass

21. LT: I can make basic constructions using a straightedge and a compass
Check It Out! Example 2
Sketch, draw, and construct a segment congruent to JK.
Step 1 Estimate and sketch. Estimate the length of JK and sketch PQ approximately the same length.
LT: I can make basic constructions using a straightedge and a compass

22. LT: I can make basic constructions using a straightedge and a compass
Check It Out! Example 2 Continued
Sketch, draw, and construct a segment congruent to JK.
Step 2 Measure and draw. Use a ruler to measure JK. JK appears to be 1.7 in. Use a ruler to draw XY to have length 1.7 in.
LT: I can make basic constructions using a straightedge and a compass

23. LT: I can make basic constructions using a straightedge and a compass
Check It Out! Example 2 Continued
Sketch, draw, and construct a segment congruent to JK.
Step 3 Construct and compare. Use a compass and straightedge to construct ST congruent to JK.
A ruler shows that PQ and XY are approximately the same length as JK, but ST is precisely the same length.
LT: I can make basic constructions using a straightedge and a compass

24. LT: I can make basic constructions using a straightedge and a compass
Homework
Foundation – p
Core – p ,18, 21-24, 27, 29,31
Challenge – 34
LT: I can make basic constructions using a straightedge and a compass