You will be completing more advanced constructions. It may be helpful to refer to the various properties of quadrilaterals. [br][br]*Additional tools have been provided to save time.[br][icon]/images/ggb/toolbar/mode_midpoint.png[/icon]Midpoint or Center (under the point tool [icon]/images/ggb/toolbar/mode_point.png[/icon]organizer )[br]*All four tools below are on a new organizer [br][icon]/images/ggb/toolbar/mode_orthogonal.png[/icon]Perpendicular Line[br][icon]/images/ggb/toolbar/mode_parallel.png[/icon]Parallel Line[br][icon]/images/ggb/toolbar/mode_linebisector.png[/icon]Perpendicular Bisector [br][icon]/images/ggb/toolbar/mode_angularbisector.png[/icon]Angle Bisector [br]

[b]Example 1, using the Midpoint Tool.[br][/b]Construct the midpoint of segment [i]AB[/i] by selecting the Midpoint or Center Tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_midpoint.png[/icon]. Then, select point [i]A, [/i]followed by point [i]B[/i]. The midpoint should appear in red.[br]*Hint, the midpoint or center tool is located under the point [icon]/images/ggb/toolbar/mode_point.png[/icon] menu.

[b]Example 2, using the Perpendicular Line tool. [br][/b]Construct a line perpendicular to line [i]r[/i] through point [i]Z. [/i]Select the perpendicular line tool [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon]. Then, select line [i]r[/i] followed by point [i]Z. [/i][br]

[b]Example 3, using the Parallel Line tool. [br][/b]Construct a line parallel to line [i]m[/i] through point [i]P[/i]. [br]Select the parallel line tool [icon]/images/ggb/toolbar/mode_parallel.png[/icon]. Then, select line [i]m[/i], followed by point [i]P[/i].

[b]Example 4, using the Perpendicular Bisector tool. [br][/b]Construct a perpendicular bisector of segment [i]CD[/i]. Select the perpendicular bisector tool [icon]/images/ggb/toolbar/mode_linebisector.png[/icon]. Then, select point [i]C[/i] followed by point [i]D[/i]. [br]

[b]Example 5, using the Angle Bisector Tool. [br][/b]Bisect angle [i]V[/i]. Construct a third point on angle [i]V[/i]. Then, select the angle bisector tool [icon]/images/ggb/toolbar/mode_angularbisector.png[/icon]. Finally, select 3 points that make up the angle in either a clockwise or counterclockwise fashion. [br]

[b]1. Construct a circle through three points. [/b][br][br]Construct a circle such that points [i]X, Y[/i], and [i]Z[/i] are along the circumference of the circle.[br]*Hint, this uses the same process as finding the circumcenter of a triangle. Use the new toolbar to speed up the process.

[b]2. Construct a 22.5 degree angle. [/b][br][br]Construct an angle equal to 22.5 degrees.[br]*Hint, start by constructing a 90 degree angle using perpendicular lines.

[b]3. Construct a parallelogram[/b][br]When you have constructed your parallelogram, measure all four sides to make sure that opposite sides are congruent. Then, drag your shape around to see if it remains a parallelogram. [br][br]*Hint, a parallelogram has opposite sides that are parallel.

[b]4. Construct a rhombus.[/b][br]When you have constructed your rhombus, measure all four sides. Then, drag your points around and see if your shape remains a rhombus. [br][br]*Hint, all four sides of a rhombus are congruent.

[b]5. Construct a rectangle. [/b][br]When you have constructed your rectangle, measure all four sides and angles. Then, drag your points around and see if your shape remains a rectangle.[br][br]*Hint, a rectangle has consecutive sides that are perpendicular to each other.

[b]6. Construct a kite.[/b][br][br][br]*Hint, a kite has diagonals that are perpendicular to each other but only one diagonal is bisected.

[b]7. Construct an isosceles trapezoid. [/b][br][br][br]*Hint, an isosceles trapezoid has one pair of parallel sides and one pair of opposite sides that are congruent.