1.6 Basic Constructions SOL: G4 Objectives: The Student Will …

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Presentation transcript:

1.6 Basic Constructions SOL: G4 Objectives: The Student Will … Construct congruent segments. Construct congruent angles. Construct perpendicular bisectors and angle bisectors.

Straightedge Compass Construction A ruler with no markings on it. A geometric tool used to draw circles and parts of circles called arcs. Construction A geometric figure drawn using a straightedge and a compass

Example 1: Construct Congruent Segments Given: AB Construct: CD so that CD  AB A B 1st Step: Draw a ray with endpoint C C 2nd Step: Open the compass to the length of AB 3rd Step: with the same compass setting put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D.

Example 2: Construct Congruent Angles Given: ∡A Construct: ∡S so that ∡S  ∡A 1st Step: Draw a ray with endpoint S 2nd Step: With the compass point on vertex A, draw an arc that intersects the sides of ∡A. Label the points of intersection B and C. S

Example 2: Construct Congruent Angles Given: ∡A Construct: ∡S so that ∡S  ∡A 3rd Step: With the same compass setting put the compass point on point S. Draw an arc and label it point of intersection with that intersects the ray as R. 4th Step: Open the compass to the length BC. Keeping the same compass setting, put the compass point on R. Draw an arc to locate T. 5th Step: Draw ST. S

Perpendicular Bisector 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

Example 3: Construct the Perpendicular Bisector Given: AB Construct: XY so that XY is the perpendicular bisector of AB 1st Step: Put the compass point on point A and draw a long arc. Make sure the compass is open passed the ½ mark of AB. A B 2nd Step: With the same compass setting, put the compass point on point B and draw another long arc. Label the points where the two arcs intersect X and Y. 3rd Step: Connect points X and Y. Label the midpoint of XY and AB as point M.

Example 2: Construct Angle Bisector Given: ∡A Construct: AD, the bisector of ∡A 1st Step: Put the compass on vertex A. Draw an arc that intersects the sides of ∡A. Label the points of intersection B and C. 2nd Step: Put the compass point on point C and draw an arc. With the same compass setting, draw an arc using point B. Be sure the arcs intersect. Label the point where the two arcs intersect D. 3rd Step: Draw AD. AD is the bisector of ∡A.