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If the point of concurrency of the perpendicular bisectors of a triangle lies outside the triangle what type of triangle is it?
Wiki User
∙ 13y ago
Isometric, I think
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An obtuse angled triangle.
Wiki User
∙ 13y ago
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What are properties of the circumcenter of a triangle?
When a circle is drawn around a triangle touching each of its 3 vertices the circumcenter of the triangle is found by drawing 3 perpendicular lines at the midpoint of each of its sides and where these lines intersect within the triangle is its circumcenter.Apex: A. The circumcenter is equidistant from each vertex of the triangle. B. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides. C. The circumcenter of an obtuse triangle is always outside it.
Is the orthocenter of a triangle always inside the triangle?
A Triangle's OrthocenterNo, it can be outside the triangle.
When is the orthocenter inside on or outside of the triangle?
Inside: acute angled triangleOn: right angled triangle Outside: obtuse angled triangle.
Which cannot be located outside of a triangle?
the centroid of a triangle
What conjectures in Classic or Euclidean Geometry have been proved from elementary axioms?
All the below listed conjectures (first letter C of Conjecture) can be proved using the Euclidean axioms of geometry. They can be used to teach or learn geometry. In this way one "discovers" the power of the Euglidean axioms.Some may be beyond this goal as they stand, as the definitions of key concepts is not included (e.g., centroid [C15], or "vertical" angle [C2], sometimes called a "right" angle.C1 Linear Pair: If two angles form a linear pair, then they are supplementary and total 180 degrees.C2 Vertical Angles: If two angles are vertical angles (right angles), then they are congruent.C3a Corresponding Angles: If two parallel lines are cut by a transversal, then the corresponding angles are congruent.C3b Alternate Interior Angles: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.C3 Parallel Lines: If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent.C4 Converse of Parallel Lines: If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent interior angles, or congruent exterior angles, then the lines are parallel.C5 Perpendicular Bisector: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoint.C6 Converse of Perpendicular Bisector: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.C7 Shortest Distance: The shortest distance from a point to a line is measured along the perpendicular bisector from the point to the line.C8 Angle Bisector: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.C9 Angle Bisector Concurrency: The three angle bisectors of a triangle mark the incenter.C10 Perpendicular Bisector Concurrency: The three perpendicular bisectors of a triangle mark the circumcenter.C11 Altitude Concurrency: The three altitudes of a triangle mark the orthocenter.C12 Circumcenter: The circumcenter of a triangle is equidistant from the three vertices.C13 Incenter: The incenter of a triangle is equidistant from the three sides.C14 Median Concurrency: The three medians of a triangle mark the centroid.C15 Centroid Conjecture: The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is half the distance from the centroid to the opposite side.C16 Center of Gravity: The centroid of a triangle is the center of gravity the triangular region.C17 Triangle Sum: The sum of the measures of the angles in every triangle is 180 degrees.C18 Isosceles Triangle: If a triangle is isosceles, then the base angles are congruent.C19 Converse Isosceles Triangle: If a triangle has two congruent angles, then it is isosceles.C20 Triangle Inequality: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.C21 Side-Angle Inequality: In a triangle, if one side is longer than the other side, then the angle opposite the longer side is the biggest angle.C22 Equiangular Triangle Exterior Angle: The measure of an exterior angle of an equilateral triangle is 120 degrees.C23 SSS Congruence: If three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.C24 SAS Congruence: If two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.C25 ASA Congruence: If two angles and the included side of one triangle is congruent to the corresponding two angles and the included side of another triangle, the two triangles are congruent.C26 SAA Congruence: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent.C27 Vertex Angle Bisector: In an isosceles triangle, the bisector of the vertex angle is also the altitude and median.C28 Equilateral/Equiangular Triangle: Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.C29 Quadrilateral Sum: The sum of the measures of the four interior angles of any quadrilateral is 360 degrees.C30 Pentagon Sum: The sum of the measures of the four interior angles of any pentagon is 540 degrees.C31 Polygon Sum: The sum of the interior angles of any polygon is n-2(180).C32 Exterior Angle Sum: For any polygon, the sum of the measures of the exterior angles will equal 360 degrees.C33 Equiangular Polygon: For any equiangular polygon, you can find the measure of one exterior angle by dividing 360 by the number of sides or subtracting the measure of an interior angle from 360.C34 Kite Angles: The vertex angles of a kite are congruent, the non vertex angles of a kite are also congruent.C35 Kite Diagonals: The diagonals of a kite are perpendicular.C36 Kite Diagonal Bisector: The diagonal connecting the vertex angles of a kite is perpendicular bisector of the other diagonal.C37 Kite Angle Bisector: The vertex angles of a kite are bisected by a diagonal.C38 Trapezoid Consecutive Angles: The consecutive angles between the bases of a trapezoid are supplementary.C39 Isosceles Trapezoid Conjecture: The base angles of a isosceles trapezoid are congruent.C40 Isosceles Trapezoid Diagonal Conjecture: The diagonals of an isosceles trapezoid are congruent.C41 Three Midsegments: The three midsegments of a triangle divides it into four congruent triangles.C42 Triangle Midsegment: A midsegment of a triangle is parallel to the third side and half the length of the third side.C43 Trapezoid Midsegment: The midsegment of a trapezoid is parallel to the bases and is equal in length to the averages of the lengths of the bases.C44 Parallelogram Opposite Angles: The opposite angles of a parallelogram are congruent.C45 Parallelogram Consecutive Angles: The consecutive angles of a parallelogram are supplementary.C46 Parallelogram Opposite Sides: The opposite sides of a parallelogram are parallel and congruent.C47 Parallelogram Diagonals: The diagonals of a parallelogram are bisected by one another.C48 Double Edged Straightedge: If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart, then the parallelogram formed is a rhombus.C49 Rhombus Diagonals: The diagonals of a rhombus are perpendicular and they bisect each other.C50 Rhombus Angles: The diagonals of a rhombus bisect the angles of the rhombus.C51 Rectangle Diagonals: The diagonals of a rectangle are bisectors to each other and are congruent.C52 Square Diagonals: The diagonals of a square bisect each other, bisect the angles, and are congruent.C53 Tangent Conjecture: A tangent to a circle is perpendicular to the radius drawn to the point of tangency.C54 Tangent Segments Conjecture: Tangent segments to a circle from a point outside the circle are congruent.
Which points of concurrency may lie outside the triangle?
The orthocentre (where the perpendicular bisectors of the sides meet).
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 kind of triangle do the perpendicular bisectors intersect in a point outside the triangle?
a right triange
Is the three perpendicular bisector of a triangle intersect at a point in the exterior of the triangle true or false?
The three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.
What is the name of the point at which all of the triangle's perpendicular bisectors intersect?
Circumcenter, this is the center-point of a circle circumscribed around the triangle. If the triangle is obtuse, then this point is outside the triangle and if the triangle is a right triangle, then the point is the midpoint of the hypotenuse.
Is it true that the point of concurrency of any triangle only happens inside the triangle?
Depends on the point of concurrency of what. The point of concurrency of altitudes will be outside in any obtuse triangle.
When is the point of concurrency outside a triangle?
When you have and obtuse triangle and you are trying to find the Orthocenter
What are properties of the circumcenter of a triangle?
When a circle is drawn around a triangle touching each of its 3 vertices the circumcenter of the triangle is found by drawing 3 perpendicular lines at the midpoint of each of its sides and where these lines intersect within the triangle is its circumcenter.Apex: A. The circumcenter is equidistant from each vertex of the triangle. B. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides. C. The circumcenter of an obtuse triangle is always outside it.
How do you find the altitude outside of a triangle?
The altitude of a triangle is the distance from the line containing the base to the vertex. Draw the base and continue on outside of the triangle. Measure perpendicular from that line to the vertex.
Do the altidudes of a triangle always meet in the interior of the triangle?
In a obtuse triangle, the point of concurrency, where multiple lines meet, of the altitudes, called the orthocenter, is outside the triangle. In a right angle, the orthocenter lies on the vertex (corner) of the right angle. In an acute angle, the orthocenter lies inside the triangle.
What are the characteristics of orthocenter?
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It may lie inside, outside, or on the triangle depending on the type of triangle. In an acute triangle, the orthocenter lies inside the triangle; in a right triangle, it is at the vertex opposite the right angle; and in an obtuse triangle, it is outside the triangle.
Is an altitude ever outside a triangle?
Sure. If one of the base angles is more than 90 degrees, then the altitude (height) is outside the triangle. Yes. This only occurs with an obtuse triangle. Because an altitude is a line drawn from a vertex to the opposite side and is perpendicular with that opposite side, it can only occur if it is outside the triangle. Look at the triangle in related links. If you look at the vertex on the top, the only way to draw the altitude would be to draw outside the triangle.
