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Geometry 15 Basic Constructions.notebook March 25, 2013 Section 15 Basic Construction Construction use a straightedge and a compass to draw a geometric figure. Straightedge a ruler with no markings Compass a geometric tool used to draw circles and parts of circles called arcs Perpendicular Lines two lines that intersect to form right angles Perpendicular Bisector a line, segment, or ray that is perpendicular to the segment at its midpoint thereby bisecting the segment into two congruent angles. Construct congruent segments: Given: segment AB Construct: segment CD so that CD ≅ AB Step 1: Draw a ray with endpoint C Step 2: Open the compass to the same length of segment AB Step 3: With the same compass setting, put the compass on point C. Draw an arc that intersects the ray. Label the point D. Segment CD is now congruent to segment AB. 1 Geometry 15 Basic Constructions.notebook March 25, 2013 Construct Congruent Angles Given: < A Construct: < S so that < A ≅ < S Step 1: Draw a ray with endpoint S Step 2: With the compass point on point A, draw an arc that intersects both sides of < A. Label the points of intersection B and C. Step 3: With the same compass setting, put the point of the compass on point S. Draw an arc that intersects the ray and continues in the direction of the angle you are constructing. Label the point of intersection with the ray, point R. Step 4: Open the compass to the length of segment BC. Keeping the same cpmoass setting, put the compass point on point R and draw an arc that intersects your first arc. Label the point of intersection Point T. Step 5: Use a straightedge to draw ray ST. 2 Geometry 15 Basic Constructions.notebook March 25, 2013 Construct a perpendicular bisector: Given: Segment AB Construct: XY so that line XY I AB at the midpoint M of AB. Step 1: Put the compass point on point A and draw a long arc. Make sure that the opening of the compass is greater than half the length of the segment. Step 2: With the same compass setting, put the point of the compass on point B and draw another long arc. Label the points where the two arcs intersect as X and Y. Step 3: Use a straightedge to draw line XY. The point where line XY intersects segment AB is the midpoint of segment AB. 3 Geometry 15 Basic Constructions.notebook March 25, 2013 Construct and angle bisector Given: < A Construct: AX, the bisector of < A. Step 1: Put the compass point of vertex A and draw an arc that intersects both sides of < A. Label the points as B and C. Step 2: Put the compass point on point B and draw an arc. With the same compass setting, put the compass point on point C and draw an arc that intersects the first arc. Label the point where the two arcs intersect point X. Step 3: Using a straightedge, draw ray AX. 4