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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.
The slant height of a pyramid and the altitude of a pyramid are not the same thing?
True, because the slant height and the altitude, or height, of the pyramid form one leg and the hypotenuse of a triangle withing the pyramid, and the hypotenuse of a triangle is always the longest side- it is not possible for the hypotenuse to be equal to the legs of a right triangle. (It is a right triangle because an altitude is perpendicular to the base of a pyramid.)
Can an angle bisector of a triangle always intersect inside the triangle?
The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)
Do the perpendicular bisectors of a triangle always sometimes or never intersect on the triangle?
The perpendicular bisectors only intersect on the triangle when it is an isosceles right triangle.
What triangle must always have at least one angle bisector that is also a perpendicular bisector?
any isosceles triangle
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! =)
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 apothem always a perpendicular bisector of each side of a polygon?
yes
The apothem is a perpendicular bisector of each side of a regular polygon?
always
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.
The slant height of a pyramid and the altitude of a pyramid are not the same thing?
True, because the slant height and the altitude, or height, of the pyramid form one leg and the hypotenuse of a triangle withing the pyramid, and the hypotenuse of a triangle is always the longest side- it is not possible for the hypotenuse to be equal to the legs of a right triangle. (It is a right triangle because an altitude is perpendicular to the base of a pyramid.)
Can an angle bisector of a triangle always intersect inside the triangle?
The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)
Can a triangle have 2 perpendicular sides always?
Not always.
Do the perpendicular bisectors of a triangle always sometimes or never intersect on the triangle?
The perpendicular bisectors only intersect on the triangle when it is an isosceles right triangle.
