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

Warm Up

1. Find CD. 8

2. Find the coordinate of the midpoint of CD. –2

Chapter 1.6Construction

Learning Target: I can make basic constructions using a straightedge

and a compass

DefinitionsConstruction – 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

Congruent segment

http://www.mathopenref.com/constcopysegment.html



http://www.mathopenref.com/constcopysegment.html

Congruent Angles

http://www.mathopenref.com/constcopyangle.html



http://www.mathopenref.com/constcopyangle.html

Perpendicular Bisector

http://www.mathopenref.com/constbisectline.html



http://www.mathopenref.com/constbisectline.html

Angle Bisector

http://www.mathopenref.com/constbisectangle.html



http://www.mathopenref.com/constbisectangle.html

Construct a trianglegiven three line segments

http://www.mathopenref.com/consttrianglesss.html



http://www.mathopenref.com/consttrianglesss.html

Assignment

Homework: P. 46 #1,2,5-16

Challenge #17 and #18 (a point each)



Step 2: Open the compass to the length of KM.

Construct TW congruent to KM.

Step 1: Draw a ray with endpoint T.

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



Construct Y so that Y G.

Step 1: Draw a ray with endpoint Y.

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°



(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.



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.

Prove by construction why you cannot construct a

perpendicular bisector with a compass opening less than AB. 12

Step 1: Put the compass point on

point A and draw a short arc. Make

sure that the opening is less than AB.12



–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 BWR Angle Addition Postulatem 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.



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.

Construct MX, the bisector of M.



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.



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.



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



Example 2 Continued


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 3.5 in.

X Y



Example 2 Continued


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.



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.



Check It Out! Example 2 Continued

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.




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.

Check It Out! Example 2 Continued




Homework

• Foundation – p. 46 7-16

• Core – p. 46 17,18, 21-24, 27, 29,31

• Challenge – 34



Documents

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