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How many medians altitudes angle bisectors and perpendicular bisectors does a triangle have?
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∙ 13y ago
medians-3
altitudes-3
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∙ 13y ago
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What kind of triangle will be produced if one of its medians is perpundicular to the opposite side of that triangle?
In an isosceles triangle, one of the medians is perpendicular to the opposite side of that triangle. In an equilateral triangle, all three medians are perpendicular to the sides of that triangle.
The point of concurrency of the medians of a triangle?
the centroid. here are all the points of concurrency: perpendicular bisector- circumcenter altitudes- orthocenter angle bisector- incenter median- centroid hope that was helpful :)
What is the purpose of an orthocenter?
In short, the orthocenter really has no purpose. There are 4 points of Concurrency in Triangles: 1) The Centroid - the point of concurrency where the 3 medians of a triangle meet. This point is also the triangle's center of gravity. 2) The Circumcenter - the point of concurrency where the perpendicular bisectors of all three sides of the triangle meet. This point is the center of the triangle's circumscribed circle. 3) The Incenter - the point of concurrency where the angle bisectors of all three angles of the triangle meet. Like the circumcenter, the incenter is the center of the inscribed circle of a triangle. 4) The Orthocenter - the point of concurrency where the 3 altitudes of a triangle meet. Unlike the other three points of concurrency, the orthocenter is only there to show that altitudes are concurrent. Thus, bringing me back to the initial statement.
Point of intersection of medians in a triangle?
The point where the three medians of a triangle intersect is called the centroid of the triangle.
Do the medians of a triangle always intersect inside the triangle?
Yes.
What kind of triangle has three angle bisectors that are also altitudes and medians?
Equilateral
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 are the number of lines of symmetry in an equilateral triangle?
The three lines joining each vertex to the midpoint of the opposite side. They are also the medians, altitudes and perpendicular bisectors of the sides. In an equilateral triangle these are coincident.
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.
Name all types of triangles for which the point of concurrency is inside the triangle?
The answer depends on what point of concurrency you are referring to. There are four segments you could be talking about in triangles. They intersect in different places in different triangles. Medians--segments from a vertex to the midpoint of the opposite side. In acute, right and obtuse triangles, the point of concurrency of the medians (centroid) is inside the triangle. Altitudes--perpendicular segments from a vertex to a line containing the opposite side. In an acute triangle, the point of concurrency of the altitudes (orthocenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Perpendicular bisectors of sides--segments perpendicular to each side of the triangle that bisect each side. In an acute triangle, the point of concurrency of the perpendicular bisectors (circumcenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Angle bisectors--segments from a vertex to the opposite side that bisect the angles at the vertices. In acute, right and obtuse triangles, the point of concurrency of the angle bisectors (incenter) is inside the 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 is a way to remember the points of concurrency Orthocenter Circumcenter Incenter and Centroid?
All Of : Altitudes - OrthocenterMy Children: Medians - CentroidAre Bringing In: Angle Bisectors - IncenterPeanut Butter Cookies: Perpendicular Bisectors - Circumcenter
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.
What kind of triangle will be produced if one of its medians is perpundicular to the opposite side of that triangle?
In an isosceles triangle, one of the medians is perpendicular to the opposite side of that triangle. In an equilateral triangle, all three medians are perpendicular to the sides of that triangle.
Are the angle bisectors of a regular polygon sometimes concurrent?
The angle bisectors of a regular polygon are always concurrent. And the point that they meet at is also the meeting point of the perpendicular bisectors of the sides. If it is a polygon with an odd nmber of sides, the "medians" [line from vertex to mid-point of opposite side] and "altitudes" [perpendicular from vertex to opposite side] will also meet at the same point.
What is the intersection of the medians called?
Intersection of Medians-Centroid Intersection of Altitudes-Orthocentre
What are the properties of an equilateral triangle?
Equilateral triangles have, by definition, 3 equal sides. This means they also have 3 equal angles (i.e. they are equiangular) with each angle measuring 60 degrees. They have 3 lines of symmetry from each vertex to the midpoint of the opposite side. These lines are the medians, perpendicular bisectors, altitudes, and angle bisectors of the triangle. The point where these three lines intersect is the centroid, incenter, circumcenter, and orthocenter of the triangle. The area of an equilateral triangle is sqrt(3)/4*s where s is the side length of the triangle.
