Investigation: Constructing an Angle Bisector

The arcs must intersect in order to connect to the vertex of the angle. Explanation: When constructing an angle bisector, we open our compass to any width, and place the point of the compass on the vertex of the angle.

the reason that the compass opening has to be greater than 1/2 of the segment is so it can make arcs. and the arcs would have to cross in the middle so that when go to draw the line it would be straight.

The steps for constructing the bisector of an angle using only a compass and a straightedge are as follows,

• Step 1 : Place the compass on the vertex of the angle.
• Step 2 : Set the compass on the vertex and adjust it to any length.
• Step 3 : Draw arcs on both sides ( rays ) of the angle.
• Step 4 :
• Step 5 :

Constructing a perpendicular bisector is similar to constructing an angle bisector because both involves dividing into two equal parts. When constructing both a perpendicular bisector and an angle bisector, the tip of the compass is placed at the end of the line to make arcs of equal radius.

1. Draw an angle on your paper. Make sure one side is horizontal.
2. Place the pointer on the vertex. Draw an arc that intersects both sides.
3. Move the pointer to the arc intersection with the horizontal side.
4. Connect the arc intersections from #3 with the vertex of the angle.

Divide the number of degrees in half. An angle bisector divides an angle into two equal parts. So, to find where the angle bisector lays, divide the number of degrees in the angle by 2. . So, the angle bisector is at the 80-degree mark of the angle.

The Angle-Bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides. The following figure illustrates this. The Angle-Bisector theorem involves a proportion — like with similar triangles.

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. to create similar triangles. 2. An angle bisector is a ray in the interior of an angle forming two congruent angles.

A line that splits an angle into two equal angles. (“Bisect” means to divide into two equal parts.)

The angle bisector of an angle of a triangle is a straight line that divides the angle into two congruent angles. The three angle bisectors of the angles of a triangle meet in a single point, called the incenter . The incenter is equidistant from the sides of the triangle. That is, PI=QI=RI .

The CIRCUMCENTER of a triangle is the point in the plane equidistant from the three vertices of the triangle. The CIRCUMCENTER of a triangle is the point in the plane equidistant from the three vertices of the triangle.

The centroid of a triangle is the point at which the three medians meet. The orthocenter is the point of intersection of the altitudes of the triangle, that is, the perpendicular lines between each vertex and the opposite side.

The centroid theorem states that the centroid is 23 of the distance from each vertex to the midpoint of the opposite side.

Centroid of a Triangle

1. Definition: For a two-dimensional shape “triangle,” the centroid is obtained by the intersection of its medians.
2. The centroid of a triangle = ((x1+x2+x3)/3, (y1+y2+y3)/3)
3. To find the x-coordinates of G:
4. To find the y-coordinates of G:
5. Try This: Centroid Calculator.

There is no direct formula to calculate the orthocenter of the triangle. It lies inside for an acute and outside for an obtuse triangle. Altitudes are nothing but the perpendicular line ( AD, BE and CF ) from one side of the triangle ( either AB or BC or CA ) to the opposite vertex.

The centroid of a triangle is the intersection of the three medians, or the “average” of the three vertices. It has several important properties and relations with other parts of the triangle, including its circumcenter, orthocenter, incenter, area, and more. The centroid is typically represented by the letter G.

To find the centroid of any triangle, construct line segments from the vertices of the interior angles of the triangle to the midpoints of their opposite sides. These line segments are the medians. Their intersection is the centroid.

The coordinates of the centroid are simply the average of the coordinates of the vertices. So to find the x coordinate of the orthocenter, add up the three vertex x coordinates and divide by three. Repeat for the y coordinate.