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In What Type Of Triangle Are The Angle Bisectors Also The Altitude And Medians Of The Triangle?
In an equilateral triangle, the angle bisectors, altitudes, and medians all coincide. This is because all sides and angles are equal, resulting in symmetrical properties that allow these segments to overlap. Therefore, in an equilateral triangle, each of these segments divides the triangle into two smaller triangles of equal area and shape.
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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 third secondary parts of a triangle?
In a triangle, the three secondary parts are the medians, altitudes, and angle bisectors. Medians connect each vertex to the midpoint of the opposite side, altitudes are perpendicular lines dropped from each vertex to the opposite side, and angle bisectors divide each angle into two equal parts. These segments play crucial roles in various geometric properties and theorems related to triangles.
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.
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
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 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 third secondary parts of a triangle?
In a triangle, the three secondary parts are the medians, altitudes, and angle bisectors. Medians connect each vertex to the midpoint of the opposite side, altitudes are perpendicular lines dropped from each vertex to the opposite side, and angle bisectors divide each angle into two equal parts. These segments play crucial roles in various geometric properties and theorems related to triangles.
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.
What set of reflections would carry triangle ABC onto itself?
To carry triangle ABC onto itself through reflections, you can use the reflections across its medians, angle bisectors, or altitudes. Specifically, reflecting across the angle bisectors of the triangle will map each vertex to the opposite side, preserving the triangle's shape. Additionally, reflecting across the perpendicular bisectors of the triangle's sides will also result in the triangle being mapped onto itself. These reflections maintain the congruence and orientation of the triangle.
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.
