Unit 1Geometry Constructions 1. Regular Hexagon Construct a hexagon, with sides lengths equal to the radius of circle C. Steps: 1. create a line passing through C and intersects the circle C at A and B. 2. Create a circle centered at A with radius AC, this circle intersects the circle C at D and E. 3. Create a circle centered at B with radius BC, this circle intersects the circle C at F and G. c 4. Connect AD, AE, BF, BG, DF, EG to create a regular Hexagon ADFBGE 2. A. Inscribed Equilateral Triangle B. Equilateral triangle with side length equals to radius Construct an equilateral triangle with side lengths equal to the radius of circle C. c Steps: --- follow process 1 to create a regular hexagon ADFBGE. Connect every the other vertex (diagonal) AF, FG, AG to create equilateral triangle AFG which is inscribed in the circle ---- follow Hexagon process 1, triangle ADC, AEC, FCB, BGC, CDF, CEG are all equilateral triangles with side length equals to radius 3. Perpendicular Bisector for line segment AB
Construct a perpendicular bisector to segment AB. A B Steps: 1. Create a circle centered at A with radius AB 2. Create a circle centered at B with radius AB 3. Circle A and Circle B intersects at D and E 4. Connect DE, DE is the perpendicular bisector of AB 5. DE intersect AB at C. AC=BC 4. Perpendicular line to a segment with a point on the line Construct a line perpendicular to line L, through point C. C e Steps: 1. Create a circle centered at point C, that intersects line m 2 times. Label those intersections as point A and B. -Start to follow process 3 2. Create a circle centered at A with radius AB 3. Create a circle centered at B with radius AB 4. Circle A and Circle B intersects at D and E 5. Connect DE, DE passes through C and is the perpendicular bisector of AB 5. Perpendicular line to a segment with a point out of the line C m Steps: 1. Create a circle centered at point C, that intersects line m 2 times. Label those intersections as point A and B. Start to follow process 3 2. Create a circle centered at A with radius AB 3. Create a circle centered at B with radius AB 4. Circle A and Circle B intersects at D and E 5. Connect DE, DE passes through C and is the perpendicular bisector of AB 6. Angle Bisector Construct an angle bisector for angle CAT. Steps: 1. Create a circle centered at point B, that intersects line AB at D and
· A B intersects line BC at E . Start to follow process 3 C 2. Create a circle centered at D with radius DE 3. Create a circle centered at E with radius DE 4. Circle D and Circle E intersects at F and G 5. Connect FG, FG passes