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What is statement of an angle bisector divides an angle into two congruent parts?
An angle bisector is a line, or a portion of a line, that divides an angle into two congruent angles, each having a measure exactly half of the original angle. Every angle has exactly one angle bisector….1.11: Congruent Angles and Angle Bisectors.
| Label It | Say It |
|---|---|
| ∠ABC≅∠DEF | Angle ABC is congruent to angle DEF. |
What are congruent angles across from each other?
Congruent angles are angles with exactly the same measure.
Does bisector create congruent angles?
The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.
Which angle is congruent to 2?
Two angles are congruent if they have the same measure. You already know that when two lines intersect the vertical angles formed are congruent….Geometry.
| Statements | Reasons | |
|---|---|---|
| 1. | ?BD is the angle bisector of?ABC | Given |
| 2. | ?ABD ~=?DBC | Definition of angle bisector |
| 3. | m?ABD = m?DBC | Definition of |
Do all angles have bisectors?
Every angle has exactly one angle bisector. An angle bisector divides an angle into three congruent angles.
What tools do you need to construct a congruent angle?
The first tool that you need for constructing a congruent angle is a compass. Compasses come in a variety of styles. Some very inexpensive ones have a simple slot for you to insert a pencil. Some more expensive and accurate compasses have a variety of lead or ink inserts that may be interchangeable.
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. DC and DA are also the radii of the circle. Since all radii of a circle have equal measure, line BD bisects the angle.
How to calculate the angle of a circle?
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. Draw two separate arcs of equal radius using both points D and E as centers. Make sure the radius is long enough so the arcs of the two circles can intersect at point F.
Which is the bisector of an angle tangent to a circle?
Based 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.
Which is the angle bisector for point D?
In the figure above, point D lies on bisector BD of angle ABC. The distance from point D to the 2 sides forming angle ABC are equal. So, DC and DA have equal measures. Conversely, 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.