Relevant Vocabulary. The MIDPOINT of a segment is a point that divides a segment into 2 = or parts.

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1 im 9: How do we construct a perpendicular bisector? Do Now: 1. omplete: n angle bisector is a ray (line/segment) that divides an into two or parts. 48 Geometry 10R 2. onstruct and label D, the bi sector of. Relevant Vocabulary Two lines (segments, rays) are PERPENDIULR ( angle. ) if they intersect to form a Ex. a) Draw and label: D, and D intersect at E. b) Name all right angles in the diagram you drew. The MIDPOINT of a segment is a point that divides a segment into 2 = or parts. Ex. Draw and label: L is the midpoint of XY. SEGMENT ISETOR passes through the of a segment. Ex. Draw and label: is a segment bisector of XY, but is not to XY. The PERPENDIULR ISETOR of a line segment is perpendicular to a segment at its midpoint. Ex. Draw and label: is the perpendicular bisector XY; M is the midpoint of XY.

2 ONSTRUTION #4: ONSTRUT THE PERPENDIULR ISETOR OF LINE SEGMENT Experiment with your construction tools to establish a construction that results in the perpendicular bisector. [Hint: Use what you know about constructing an equilateral triangle.] linebisect.html Steps 1. Draw circle(arc), center, radius more than ½. 2. Draw circle(arc), center, using same radius as in step (1). 3. Label the points of intersection created by steps (1) and (2) as and D. 4. Draw D. Practice: onstruct the perpendicular bisector of D. Label the midpoint M and label the perpendicular bisector as EF. Name one right angle: D

3 Ex a) Draw point equidistant from points and. b) Draw point D equidistant from points and. c) Draw point E equidistant from points and. point is EQUIDISTNT from two given points if it is the same distance from both given points. d) How many points could you draw equidistant from and? ctivity: DE is the perpendicular bisector of. (, D, and E are collinear.) Using your compass, what conclusion can you make about the following pairs of segments? 1) and 2) D and D 3) E and E ased on your findings, fill in the observation below. ny point on the perpendicular bisector of a line segment is from the endpoints of the line segment. ONSTRUTION #5: ONSTRUT PERPENDIULR TO LINE FROM POINT NOT ON THE LINE We will now construct a perpendicular line to line l from a point X not on line l. omplete the construction and the steps of the construction outlined below. l X 86 0 Step 1: Draw circle(arc) X so that the circle intersects line l in two points. Step 2: Label the two points of intersection as and. Step 3: Draw circle(arc) and circle(arc), same radius as Step 1. Step 4: Label the intersection of circle and circle as D. Step 5: Draw the perpendicular bisector: line.

4 Exercises 1. Divide segment into 4 segments of equal length. 2. onstruct parallel lines l 1 and l 2 as follows: Step 1: onstruct line l 3 which will be perpendicular to line l 1 from point Step 2: onstruct line l 2 which will be perpendicular to l 3 through point. (Hint: This is the same as bisecting a straight angle.) l 1

5 3. Here is another method for constructing a line parallel to a given line through a point not on the line, not using perpendicular lines. Using the construction for copying an angle, construct a line parallel to line L through point P. P L 4a) onstruct the perpendicular bisector of. b) onstruct the angle bisector of. Let's Sum it Up!! perpendicular bisector of a segment passes through the of the segment and forms angles with the segment. (Mark the diagram to show this.) point is said to be equidistant from two different points and if =. (Mark the diagram to show this.)

6 onstruction of a perpendicular to a line from a point not on the line - arcs (not full circles) l step 3 step 1 step 2 step 2

7 Name Date Geometry R HW #9 onstructing a Perpendicular isector 1. onstruct the perpendicular bisector of the segments below. L M 2. onstruct the line perpendicular to line l through point. Number the steps in the correct order, from 1-5. Draw circle(arc) : center and circle (center ), using two equal radii that intersect. Draw D. l Label D, the intersection of arcs and. Label the two points of intersection as and. Draw circle(arc): center, intersecting l in two points. 3. onstruct the perpendicular bisectors of,, and on the triangle below. What do you notice about the segments you have constructed? OVER

8 4. Two homes are built on a plot of land. oth homeowners have dogs, and are interested in putting up as much fencing as possible between their homes on the land, but in a way that keeps the fence equidistant from each home. Use your construction tools to determine where the fence should go on the plot of land. H 2 H 1 Review 5. In Δ, =. If = x 2 + 8x, = 3x + 5 and = 20. a) Draw an appropriate diagram. b) Write and solve a quadratic equation for x. c) Find the perimeter of Δ. 6. In the diagram below, = 8x 15, D = 2x + 12 and D = 4x + 9. Find m D. 7. Find the variables. c o a o 83 o do f o b o g o e o 56 o a = b = c = d = e = f = g =