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In what type of triangle are the angle bisectors also the altitudes and medians of a triangle?
In an equilateral triangle, the angle bisectors are also the altitudes and medians. This is because all sides and angles are equal in an equilateral triangle, leading to a symmetry where the angle bisector from any vertex also serves as the median (dividing the opposite side into two equal segments) and the altitude (perpendicular to the opposite side). Thus, each of these segments coincides in an equilateral triangle.
What are the three lines of symmetry on an equilateral triangle?
They are the lines joining each of the vertices to the mid-points of the opposite sides. In an equilateral triangle, these lines are the medians, angle bisectors, altitudes and perpendicular bisectors of the sides - all in one!
What is the measure of a 45-45-90 triangle if the hypotenuse is 12?
It depends on what you mean by "measure": perimeter or area, or lengths of medians perhaps, or angle bisectors.
What are the lines of symmetry on a regular polygon triangle?
A regular polygon triangle is an equilateral triangle. It has three lines of symmetry: a line passing through each vertex and the mid-point of the opposite side. These are the three medians or altitudes or perpendicular bisectors or angle bisectors of the triangle - they are all the same lines.
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.)
How many medians altitudes angle bisectors and perpendicular bisectors does a triangle have?
medians-3 altitudes-3
What kind of triangle has three angle bisectors that are also altitudes and medians?
Equilateral
What do you call to a line of symmetry of an isosceles triangle?
There is no specific name. It is one of the medians, angle bisectors and perpendicular bisectors: one set of these is coincident and is the line of symmetry.
What are the three lines of symmetry on an equilateral triangle?
They are the lines joining each of the vertices to the mid-points of the opposite sides. In an equilateral triangle, these lines are the medians, angle bisectors, altitudes and perpendicular bisectors of the sides - all in one!
What is the measure of a 45-45-90 triangle if the hypotenuse is 12?
It depends on what you mean by "measure": perimeter or area, or lengths of medians perhaps, or angle bisectors.
What are the lines of symmetry on a regular polygon triangle?
A regular polygon triangle is an equilateral triangle. It has three lines of symmetry: a line passing through each vertex and the mid-point of the opposite side. These are the three medians or altitudes or perpendicular bisectors or angle bisectors of the triangle - they are all the same lines.
Angle bisector of a triangle?
The angle bisectors of a triangle are the lines which cut the inner angles of a triangle into equal halves. The angle bisectors are concurrent and intersect at the center of the incircle.
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.)
What is the name of the point at which all of a triangle's angle bisectors converge?
The name of the point at which all of a triangle's angle bisectors converge is the incenter.
At what point are the angle bisectors of a triangle concurrent?
Angle bisectors intersect at the incenter which is equidistant from the sides
What is the point in a triangle where all three angle bisectors meet?
The point in a triangle where all three angle bisectors meet is called the incenter.
Are the medians of a triangle equidistant from each vertex?
Every triangle has three medians, just like it has three altitudes, angle bisectors, and perpendicular bisectors. The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides. The point of intersection of all three medians is called the centroid of the triangle. The centroid of a triangle is twice as far from a given vertex than it is from the midpoint to which the median from that vertex goes. For example, if a median is drawn from vertex A to midpoint M through centroid C, the length of AC is twice the length of CM. The centroid is 2/3 of the way from a given vertex to the opposite midpoint. The centroid is always on the interior of the triangle.
