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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.
Does a line segment bisector always be perpendicular to the original irie?
Not sure what an "irie" is. But a bisector does not need to be perpendicular.
What is right bisector in math?
A right bisector of a line segment, is better know as a perpendicular bisector. It is a line that divides the original line in half and is perpendicular to it (makes a right angle).
Can bisector of angle divide the triangle into similar triangle?
Given certain triangles, it would be possible for an angle to be bisected and create two new triangles which are similar to each other. And in the case of a [45°, 45°, 90°] right triangle, if you bisect the right angle, then you will create two new [45°, 45°, 90°] triangles (both similar to each other and similar to the original).
What is a congruence statement?
The two angles in which the bisector has split the original angle into.
Angles formed by an angle bisector?
They are half the original angle, whatever that was.
What is the approximate length of the base of an isosceles triangle if the congruent sides are 3 feet and the vertex angle is 35 degress?
The median of an isosceles triangle from its apex is also the perpendicular bisector of the base. This line divides the triangle into two congruent right angled triangles whose hypotenuse is 3 feet and whose apical angle is 35/2 = 17.5 degrees. If the base of the original triangle was 2b cm then sin(17.5) = b/3 so that b = 3*sin(17.5) = 0.9cm so that the base was 2b = 1.8 feet Alternatively, you could use the sine rule on the triangle:
Can you have line of symmetry but not rotational symmetry?
Yes, it is possible to have a shape that has a line of symmetry but does not have rotational symmetry. An example is the letter "K", which has a vertical line of symmetry but cannot be rotated to match its original orientation.
What is angular bisector?
It is a line that goes through the vertex of the angle and divides the original angle into halves.
When the vertex angle and the base of an isosceles triangle are given how do you find its perimeter?
Using the trigonometry ratio for the cosine and by halving the base lenght which will result in two right angled triangles. Then after working out the hypotenuse simply double it and add on the original base length.
How do you solve An isosceles triangle has a base of 22 inches and its base angles each measure 26 degrees find the length of the altitude to the base?
The altitude to the base of an isosceles triangle bisects it forming two right angled triangles (which are congruent). In either of those right angled triangles, the altitude forms one leg and half the base of the original triangle forms the other. So, tan(26) = Alt/11 or Alt = 11*tan(26) inches = 5.365 inches.
How do you find the length of a bisector in a square?
The simplest bisector is one going from the midpoint of one side of the square to the mid point of the opposite side. It is easy to show that it is the same length as the sides of the original square.
