Download Geometry 1-5 Basic Constructions.notebook

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.
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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.
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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.
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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.
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