Constructions

Don’t change your radius! Construction #1 Construct a segment congruent to a given segment. This is our compass. Given: A B Procedure: 1. Use a straightedge to draw a line. Call it l. Construct: XY = AB 2. Choose any point on l and label it X. 3. Set your compass for radius AB and make a mark on the line where B lies. Then, move your compass to line l and set your pointer on X. Make a mark on the line and label it Y. l X Y Don’t change your radius!

Construct an angle congruent to a given angle Construction #2 Construct an angle congruent to a given angle A C B Given: Procedure: D 1) Draw a ray. Label it RY. 2) Using B as center and any radius, draw an arc intersecting BA and BC. Label the points of intersection D and E. E Construct: 3) Using R as center and the SAME RADIUS as in Step 2, draw an arc intersecting RY. Label point E2 the point where the arc intersects RY D2 R Y 4) Measure the arc from D to E. E2 5) Move the pointer to E2 and make an arc that that intersects the blue arc to get point D2 6) Draw a ray from R through D2

Bisector of a given angle? Construction #3 How do I construct a Bisector of a given angle? C A B Z Given: X Y Procedure: Using B as center and any radius, draw and arc that intersects BA at X and BC at point Y. 2. Using X as center and a suitable radius, draw an arc. Using Y as center and the same radius, draw an arc that intersects the arc with center X at point Z. 3. Draw BZ.

How do I construct a perpendicular bisector to a given segment? Construction #4 How do I construct a perpendicular bisector to a given segment? X Given: A B Y Procedure: Using any radius greater than 1/2 AB, draw four arcs of equal radii, two with center A and two with center B. Label the points of intersection X and Y. 2. Draw XY

Construction #5 How do I construct a perpendicular bisector to a given segment at a given point? Z Given: C k X Y Procedure: Using C as center and any radius, draw arcs intersecting k at X and Y. Using X as center and any radius greater than CX, draw an arc. Using Y as center and the same radius, draw and arc intersecting the arc with center X at Z. 3. Draw CZ.

Construction #6 How do I construct a perpendicular bisector to a given segment at a given point outside the line? k P Given: X Y Z Procedure: Using P as center, draw two arcs of equal radii that intersect k at points X and Y. Using X and Y as centers and a suitable radius, draw arcs that intersect at a point Z. 3. Draw PZ.

Construction #7 How do I construct a line parallel to a given line through a given point? k P 1 l Given: A B Procedure: Let A and B be two points on line k. Draw PA. At P, construct <1 so that <1 and <PAB are congruent corresponding angles. Let l be the line containing the ray you just constructed.