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What are the reasons used in the proof that the angle-bisector construction can be used to bisect any angle?
The angle-bisector construction is proven effective by demonstrating that the two angles formed by the bisector are congruent. This is achieved using the properties of isosceles triangles, where the lengths of the sides opposite the equal angles are shown to be proportional to the lengths of the adjacent sides of the original angle. Additionally, the use of geometric tools like a compass and straightedge allows for the accurate replication of distances and angles, ensuring that the bisector divides the angle into two equal parts. Thus, the congruence of the resulting angles confirms that the construction reliably bisects any angle.
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What are reasons used in the proof that the angle bisector construction can be used to bisect any angle?
The angle bisector construction can bisect any angle due to the properties of congruent triangles and the equal distances from a point on the bisector to the sides of the angle. By drawing an arc from the vertex that intersects both sides, we create two segments that can be shown to be equal. Using the triangle congruence criteria (such as the Side-Angle-Side or Angle-Side-Angle postulates), we can demonstrate that the angles formed are congruent, confirming that the angle has been bisected accurately. Thus, any angle can be bisected using this construction method.
What is it called when divide an angle in two equal angle?
bisect
Does a bisector cut an angle in half?
To bisect an angle is to divide the angle in half.
Does the angle bisector in a triangle bisect the opposite side?
Not necessarily. The only time that the angle bisector would bisect the opposite side is if you were bisecting the vertex angle of an isosceles triangle.
When you divide an angle into two equal you it?
You bisect it.
Which of the following are reasons ised in the proof that the angle-bisector construction can be used to bisect any angle?
That one there!
What reasons are proof that the angle bisector construction can be used to bisect any angle?
Proposition 3 of Book IV in Euclid's Elements (angle bisector theorem)
What are reasons used in the proof that the angle-bisectors construction can be used to bisect any angle?
All of the radii of a circle are congruent CPCTC sss triangle congruence postulate
Which of the following are reasons used in the proof that the angle bisector construction can be used to bisect any angle?
-CPTCP -SSS triangle congruence postulate -all of the radii of the circle are congruent apex :)
How do you bisect an obtuse angle?
In the same way that you bisect an acute triangle. Alternatively, you could extend one of the rays of the obtuse angle so that you have an acute angle. Bisect that angle and then draw a perpendicular to the bisector of the acute angle through the vertex.
You can bisect an angle using the paper folding technique?
Yes, you can bisect an angle using the paper folding technique.
When you bisect an angle you are?
Dividing the angle into 2 congruent angles
What is it called when divide an angle in two equal angle?
bisect
Does a bisector cut an angle in half?
To bisect an angle is to divide the angle in half.
What is bisect?
A bisect splits something completely in half whether it is an angle, a line, or whatever
What does it mean for diagonals to bisect each other?
to bisect an angle means to cut it in half
Is it true that you cannot bisect an angle using paper folding constructions?
No. It is possible to fold an angle on paper to bisect it.
