Show Pencilbutton. Then, move the pencil tip over the place to mark. Finally, release the click.
A natural history museum manager hopes to place a replica of a moai statue in a triangular room in such a manner that the statue is equidistant from the walls that will have detailed diagrams and explanations. The location of the statue corresponds to the incenter of the triangle formed by the walls. This placement will allow for a clear walking path.
The following three steps can be used to draw a segment with the same length as AB.
With the straightedge, draw a new segment such that it is longer than AB.
As can be seen, AB and are copies of each other.
The following five steps can be used to draw an angle whose measure is equal to the measure of ∠ABC.
Start by tying a pencil to one end of the string and locating the other end at B. The string must be shorter than the sides of the angle.
Using the straightedge, draw This ray along with form ∠DEF whose measure is equal to the measure of ∠ABC.
Paper folding, also referred to as origami, provides an alternative method for making constructions when tools such as a compass are not on hand.
To bisect ∠ABC, the following two steps can be done. If available, it is recommended to use tracing paper.
Using the folding paper technique, the challenge presented at the beginning of the lesson can be solved. A natural history museum manager hopes to place a replica of a moai statue in a triangular room in such a manner that the statue is equidistant from the walls that will have detailed diagrams and explanations. The location of the statue corresponds to the incenter of the triangle formed by the walls. This placement will allow for a clear walking path.
The manager's son, Kevin, sees the blueprint and wants to help to locate the incenter. Unfortunately, he does not have a protractor. Can he locate the incenter on the blueprint? If so, how?
Can he locate the incenter? Yes.
How? By folding the blueprint, two different angle bisectors can be drawn. The point where the angle bisectors intersect corresponds to the incenter of the triangle.
Kevin needs to find the incenter of the triangle formed by the room's walls.
The incenter of a triangle is the point of intersection of the triangle's angle bisectors.
To obtain the point of intersection, Kevin needs to draw at least two angle bisectors to locate the incenter. To do so, begin by labeling the vertices of the triangle.
Notice that, thanks to the Incenter Theorem, the angle bisector of ∠B does not have to be drawn to locate the incenter.
To draw the perpendicular bisector of AB, the following two steps can be used. If available, tracing paper is recommended.
Math teacher by day, the world's greatest futsal coach by night, Coach Tiffaniqua drew the following formation on a board to teach her players where to position themselves when taking a free kick near the court's center.
Ali, ecstatic, asked where he should be in the formation. Coach Tiffaniqua told Ali that he should be positioned the same distance from Diego, Ignacio, and Kevin. Determine where Ali should be positioned on the futsal field.
Notice that Diego, Ignacio, and Kevin form a triangle. Thus, Ali should be positioned at a point that is equidistant from the vertices of this triangle.
The last construction of this lesson will be to draw a line perpendicular to a given line through a point that is not on the line. Of course, this can be done using a straightedge and compass. However, it is possible to do so without the use of a compass.
To draw a line perpendicular to through P the following two steps can be used.
However, Ali does not have a compass at hand. Help Ali draw the desired triangle.
To draw the altitude from A, fold the paper so that A is on the crease and the part of BC in one part of the paper falls above the other part of BC.
Before finishing the lesson, two interesting facts about the orthic triangle — also called the pedal triangle.