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

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

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

LT: I can make basic constructions using a straightedge and a compass Congruent segment http://www.mathopenref.com/constcopysegment.html LT: I can make basic constructions using a straightedge and a compass

LT: I can make basic constructions using a straightedge and a compass Congruent Angles http://www.mathopenref.com/constcopyangle.html LT: I can make basic constructions using a straightedge and a compass

Perpendicular Bisector http://www.mathopenref.com/constbisectline.html LT: I can make basic constructions using a straightedge and a compass

LT: I can make basic constructions using a straightedge and a compass Angle Bisector http://www.mathopenref.com/constbisectangle.html LT: I can make basic constructions using a straightedge and a compass

Construct a triangle given three line segments http://www.mathopenref.com/consttrianglesss.html LT: I can make basic constructions using a straightedge and a compass

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

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

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

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

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

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

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

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

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

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

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 3.5 in. X Y LT: I can make basic constructions using a straightedge and a compass

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

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

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

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

LT: I can make basic constructions using a straightedge and a compass Homework Foundation – p. 46 7-16 Core – p. 46 17,18, 21-24, 27, 29,31 Challenge – 34 LT: I can make basic constructions using a straightedge and a compass