Basic Geometric ConstructionsPart 1 C N Coln Geometry

Basic Geometric Constructions-Part 1 C. N Colón Geometry St. Barnabas High School

Objectives • Students will – Copy a segment – Copy an angle – Bisect a segment – Bisect an angle – Construct a Perpendicular Bisector of a line segment directly and from a point near a line as well as on a line.

How to Copy a Segment 1) Since a segment is a part of a line, we’ll start by drawing a ray that is somewhat longer than our intended segment, and call the starting A’. end of the 2) Place thepoint Needle compass on point A, and adjust its length to match the distance AB. 3) Without changing the width of the compass, put the Needle end of the compass on point A’, and draw the arc to cross your ray. Label the point of intersection B’. You’ve just copied AB to A’B’ A A’ B B’

Copy An Angle 4) Now go back to the original angle, 1) Since an your angleneedle is two on rays with a and put the point common vertex we’ll start of intersection of AB and by the arc. drawing a ray and call ray B’A’. Measure the distance along the C arc to the ray BC. 2) Place the Needle end of the 5) Without the width compass changing on point B, and makeofan the compass, put over your from needle arc that crosses BAon the point of intersection of the to BC. arc and B’A’. Make an arc that first arc drew 3) crosses Withoutthe changing theyou width of on this new angle. put the Needle end the compass, of thea compass B’, and 6) Draw ray fromon B’ point thru the point draw the arc crossing long of intersection of the B’A’ two arcs. enough more cross where Label a to point on than the ray as C’. B’C’ willcopied be. the angle ABC as You’ve A’B’C’. B A C’ B’ A’

Bisecting a Segment 1) Place the needle of your compass on A. Make its width more than half-way to B, and make a half-circle. 2) Without changing the width of the compass, put the needle of your compass on B. Make a half-circle that overlaps the first one. 3) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the segment AB, and is perpendicular to AB. A B

Bisecting an Angle C 1) Place the needle of your compass on B. Draw an arc that crosses both BA and BC. E 2) Label the intersection of the arc and BA “D”, and the intersection of the arc and BC “E”. 3) Place the needle of the compass on D, and set the width to match more than half the distance to E. Make a half-circle. 4) Leave the compass width as it is. Place the needle of the compass on E, and make a halfcircle overlapping the previous half-circle. 5) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the angle ABC. B D A

Perpendicular line Construction Perpendicular Bisector Aim: Divide a line in half at 90º P Perpendicular Line from a point NEAR a line Perpendicular Line from a point ON a line P

Perpendicular Bisector A Aim: Divide a line in half at 90º Rule a line (leaving some space on each side of the line) Click to start Step 1 Home

Perpendicular Bisector A Aim: Divide a line in half at 90º Compass point Set your compass to about ¾ of the line length Step 1 Home

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Set your compass to about ¾ of the line length Step 1 Home

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Step 1 Arc into space each side of the line Home

Perpendicular Bisector B Aim: Divide a line in half at 90º Keep the compass the same Arc into space each side of the line Step 1 Step 2 Compass point Home

Perpendicular Bisector Aim: Divide a line in half at 90º Keep the compass the same Arc into space each side of the line Step 1 Step 2 Compass point Home

Perpendicular Bisector Aim: Divide a line in half at 90º Arc into space each side of the line Step 1 Step 2 Compass point Home

Perpendicular Bisector C Aim: Divide a line in half at 90º Use a ruler to join this point With this point Step 1 Step 2 Step 3 Home

Perpendicular Bisector Aim: Divide a line in half at 90º Perpendicular bisector This should be 90º 1 1 2 2 And half way Step 1 Step 2 Step 3 The End Circumcircle Home

Circumcircle Do the Perpendicular Bisectors of the sides of a triangle meet at one point? This? Step 1 Step 2 Step 3 The End Circumcircle Home

Circumcircle Do the Perpendicular Bisectors of the sides of a triangle meet at one point? OR This? Step 1 Step 2 Step 3 The End Circumcircle Home

Circumcircle Do the Perpendicular Bisectors of the sides of a triangle meet at one point? Step 1 Step 2 Step 3 The End Circumcircle Home

Perpendicular Line from a Point A Aim: Construct a line at 90º through a point near a line P Rule a line Mark a point near the line (about 4 cm away is fine) Leave some space on either side of the line Click to start Step 1 Home

Perpendicular Line from a Point A Aim: Construct a line at 90º through a point near a line Compass point P Set your compass to reach over the line so the arc will cut twice Step 1 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Set your compass to reach over the line so the arc will cut twice Step 1 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Move your compass to one side Step 1 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Step 1 Home

Perpendicular Line from a Point B Aim: Construct a line at 90º through a point near a line P Step 1 Step 2 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Step 1 Step 2 Keep the compass the same Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Step 1 Step 2 Keep the compass the same Arc into space each side of the line Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Step 1 Step 2 Arc into space each side of the line Home

Perpendicular Line from a Point C Aim: Construct a line at 90º through a point near a line P Compass point Arc into space each side of the line Step 1 Step 2 Keep the compass the same Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Arc into space each side of the line Step 1 Step 2 Keep the compass the same Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Arc into space each side of the line Step 1 Step 2 Step 3 Home

Perpendicular Line from a Point D Aim: Construct a line at 90º through a point near a line Use a ruler to join this point P With this point Step 1 Step 2 Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line This should be 90º Perpendicular Line P 90º Step 1 Step 2 Step 3 The End Home

Perpendicular Line from a Point A Aim: Construct a line at 90º through a point on a line Rule a line Mark a point on the line (not in the middle) Leave some space on either side of the line P Click to start Step 1 Home

Perpendicular Line from a Point A Aim: Construct a line at 90º through a point on a line Compass point P Mark an arc on both sides of point P Step 1 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point on a line P Compass point Set compass to ¾ the length of the arc Step 1 Step 2 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point on a line Keep the compass the same P Compass point Step 1 Step 2 Arc into space each side of the line Home

Perpendicular Line from a Point C Aim: Construct a line at 90º through a point on a line Keep the compass the same P Compass point Arc into space each side of the line Step 1 Step 2 Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point on a line Keep the compass the same P Compass point Arc into space each side of the line Step 1 Step 2 Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point on a line P Compass point Arc into space each side of the line Step 1 Step 2 Step 3 Home

Perpendicular Line from a Point D Aim: Construct a line at 90º through a point on a line Use a ruler to join this point P With this point Step 1 Step 2 Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point on a line Perpendicular Line This should be 90º P Step 1 Step 2 Step 3 The End Home