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The apothem is a perpendicular bisector of each side of a regular polygon?
always
Is a perpendicular bisector always an angle bisector?
thank goodness for my math teacher, norm! he said only in an isosceles triangle. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base! =)
If a point lies on the perpendicular bisector of a segment then the point is always equidistant from the endpoints of the segment?
true
What is the formula of an apothem?
The apothem of a regular polygon? well lets look at the math behind it before i recall it... you can scroll down to the bottom of the page if you don't want to read this. the formula is on the bottom of the page * A regular polygon is made up of a sequence of isoceles triangles.. * How do we know that they are isoceles? ------1)the triangles that make up a regular polygon are congruent -------2)the radii are always congruent . the radii of a regular polygon goes from it's center to the vertices...(hint:think of a circle's radius) * due to the fact that you have isoceles triangles they have to be made by angle bisectors through the regular polygon otherwise they couldn't be congruent * okay now that we know that the triangles are isoceles we also know that the apothem is an angle bisector so it cuts the measurement of a side in half. lets use j for our the measurement of our side. * okay we got the angle measures and our apothem made two congruent triangles so now we can use trig ratios to find our apothem so the formula is a=0.5j(tan [n-2]*180/2n) where n is the # of sides and j is the measurement of a side or you can simplify that to a=0.5j(tan [n-2]*90/n) i am using degrees for my angle meausure by the way
A polygon with only 1 pair of perpendicular sides?
A polygon with only 1 pair of perpendicular sides is called a trapezoid. In a trapezoid, one pair of opposite sides are parallel, while the other pair are not parallel and intersect at a right angle. The sum of the interior angles of a trapezoid is always 360 degrees. Examples of trapezoids include isosceles trapezoids, right trapezoids, and scalene trapezoids.
The apothem is a perpendicular bisector of each side of a regular polygon?
always
Is the radius of a regular polygon always greater than the apothem?
yes the radius of a regular polygon is always greater than the apothem
Is a protractor necessary to construct a perpendicular bisector?
Not always because a perpendicular bisector can be constructed with compasses
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.
Is the altitude of a triangle always the perpendicular bisector?
No.
Is a circle can not form a perpendicular bisector?
A circle itself does not form a perpendicular bisector because a perpendicular bisector is a line that divides a segment into two equal parts at a right angle, typically associated with straight segments. However, the concept of a perpendicular bisector can be applied to chords within a circle. The perpendicular bisector of a chord will always pass through the center of the circle.
Is a perpendicular bisector always an angle bisector?
thank goodness for my math teacher, norm! he said only in an isosceles triangle. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base! =)
Which types of triangles must always have at least one angle bisector that is also a perpendicular bisector?
iscoceles triangle! =)
What triangle must always have at least one angle bisector that is also a perpendicular bisector?
any isosceles triangle
Must a bisector of a segment always be a perpendicular line?
Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.
In a circle the perpendicular bisector of a chord must pass through the center of the circle?
Yes, in a circle, the perpendicular bisector of a chord does indeed pass through the center of the circle. This is because the perpendicular bisector of a chord divides it into two equal segments and is equidistant from the endpoints of the chord. Since the center of the circle is the point that is equidistant from all points on the circle, it must lie on the perpendicular bisector. Thus, any chord's perpendicular bisector will always intersect the center of the circle.
Does a perpendicular bisector of a triangle always passes through the opposite vertex?
No, the perpendicular bisector of a side of a triangle does not necessarily pass through the opposite vertex. The perpendicular bisector is a line that is perpendicular to a segment at its midpoint, and it may intersect the interior or exterior of the triangle, depending on its shape. In fact, the only time a perpendicular bisector passes through the opposite vertex is in the case of an isosceles triangle, where the two sides are equal, and their perpendicular bisectors coincide with the altitude.
