Introduction To Constructions

Explore the Geogebra Tools
Use the Compass Tool to make a circle with a center at A and a radius the length of A to B.[br][list][*]Click the tool at the top.[/*][*]Click Point A[/*][*]Click Point B[/*][*]Move the mouse, and the mouse is now the center of the circle.[/*][*]Click Point A to place the circle you made there.[br][/*][/list]
Construct a Segment CD congruent to Segment AB
[b]Step 1: [/b]Use the compass to create a circle with a Center at Point A and a radius the length of Segment AB.[br][b]Step 2: [/b]Move the circle down to Point C, creating a circle with a center at Point C.[br][b]Step 3: [/b]Place a new Point D, any where on Circle C.[br][b]Step 4: [/b]Construct a segment from Point C to Point D.[br][b]Step 5: [/b]Use the measurement tool to confirm that Segment CD is the same length as Segment AB.
Construct a Perpendicular Bisector to Segment AB
[b]Step 1: [/b]Use the compass to create a circle with a Radius the length of AC and a center at Point A.[br][b]Step 2: [/b]Use the compass to create a circle with a Radius the length of AC and a center at Point B.[br][b]Step 3: [/b]Use the intersection tool to mark the intersection points of Circle A and Circle B.[br][list][*]Move your mouse to Circle A and it will become bold, click it, and then do the same to Circle B and then the intersection points will appear.[br][/*][/list][b]Step 4: [/b]Use the line creator tool to draw a line through points D and E.[br][b]Step 5: [/b]Use the angle measure tool to confirm that line DE and Segment AB are in fact perpendicular.[br][list][*]Click Line DE and then Click Segment AB and the angle tool will measure the angle between the two lines.[/*][/list][b]Step 6[/b]: Use the intersection tool to mark Point F as the intersection of line DE and Segment AB.[br][list][*]Click Line DE and Click Segment AB and the point of intersection will appear as Point F.[/*][/list][b]Step 6: [/b]Use the measurement tool to confirm that Segment AF and Segment FB are congruent.
Construct a Line Parallel to Line AB
[b]Step 1: [/b]Connect points C and D to make Line CD.[br][b]Step 2: [/b]Use the Circle Radius tool to construct a circle with a center at Point D and a radius of 2.[br][b]Step 3: [/b]Use the Circle Radius tool to construct a circle with a center at Point C and a radius of 2.[br][b]Step 4: [/b]Use the intersection tool to mark the intersections of Circle D with Line CD and the intersection of Circle D with Line AB. [br][b]Step 5: [/b]Use the intersection tool to mark the intersections of Circle C with Line CD.[br][b]Step 6: [/b]Use the Compass to measure the distance between points F and H and move the circle up to have a center at Point I.[br][list][*]Your letters might be different than mine... you're using the compass to create a circle with a radius the length of the acute angle of Circle D and then moving it up to have a center at the point on line CD furthest away from segment AB.[/*][/list][b]Step 7[/b]: Use the intersection tool to mark the intersections of Circle I and Circle C as Point L.[br][b]Step 8: [/b]Use the line tool to create a line between points C and L. [br][list][*]Your letters might be different, point L should be the point that is the intersection of Circle I and Circle C, on the right of Line CD.[br][/*][/list][b]Step 9[/b]: Use the slope tool to verify that line CJ and Line AB are Parallel.
Extension
Using what you learned during this discovery, can you construct multiple perpendicular lines to segment AB? Be prepared to defend how you know the lines are perpendicular.

Information: Introduction To Constructions