Referencing the diagram below, the three bisecting rays intersect at point D. The point at which the three interior angle bisectors intersect is known as the incenter of the triangle. Angle bisector theoremįor a triangle, like the one in the diagram below, if the bisector of angle A intersects side BC at point D, the ratio of the lengths of AB to AC equals the ratio of the length BD to DC. Since all radii of a circle have equal measure, line BD bisects the angle. DC and DA are also the radii of the circle. In the diagram above, the two sides of the angle are tangent to the circle and, DC and DA are the distances from the center of the circle to the sides. So, DC and DA have equal measures.Ĭonversely, if a point on a line or ray that divides an angle is equidistant from the sides of the angle, the line or ray must be an angle bisector for the angle.īased on the equidistance theorem, it can be seen that when the two sides that make up an angle are tangent to a circle, the line segment or ray formed by the angle's vertex and the circle's center is the angle's bisector. The distance from point D to the 2 sides forming angle ABC are equal. In the figure above, point D lies on bisector BD of angle ABC. If a point lies anywhere on an angle bisector, it is equidistant from the 2 sides of the bisected angle this will be referred to as the equidistance theorem of angle bisectors, or equidistance theorem, for short. Use a ruler to draw a straight ray from O to F.Make sure the radius is long enough so the arcs of the two circles can intersect at point F. Draw two separate arcs of equal radius using both points D and E as centers.Place the point of the compass on vertex, O, and draw an arc of a circle such that the arc intersects both sides of the angle at points D and E, as shown in the above figure.In geometry, it is possible to bisect an angle using only a compass and ruler. Bisecting an angle with compass and ruler Since TV bisects ∠UTS, ∠UTV = ∠STV and ∠UTS = ∠UTV + ∠STV, so ∠UTS = 60° + 60° = 120°.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |