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Yes
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No. A median is a line from a vertex to the midpoint of the opposite side. It divides the triangle into congruent parts only if
the triangle is equilateral
or
if the triangle is isosceles and it is the median from the unequal vertex.
In all other cases the two parts will not be congruent.
What else can I help you with?
If the median to a side of a triangle is also an altitude to that side then the triangle is isosceles How do you write this Proof?
Let the triangle be ABC and suppose the median AD is also an altitude.AD is a median, therefore BD = CDAD is an altitude, therefore angle ADB = angle ADC = 90 degreesThen, in triangles ABD and ACD,AD is common,angle ADB = angle ADCand BD = CDTherefore the two triangles are congruent (SAS).And therefore AB = AC, that is, the triangle is isosceles.
In an isosceles triangle what are the altitude and media?
In an isosceles triangle, the altitude from the vertex angle to the base bisects the base and is also the median, as it divides the triangle into two congruent right triangles. This altitude is perpendicular to the base, creating two equal segments. Consequently, in an isosceles triangle, the altitude, median, and angle bisector from the vertex angle to the base are all the same line segment.
Which segment always divides a triangle into two triangles of equal areas?
median
How is the altitude and a median of a triangle the same?
they are the same because the triangles side is equal
How does the triangle above show that medians bisect the sides of a triangle?
A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. In the triangle, the medians divide the triangle into two smaller triangles of equal area, demonstrating that each median intersects the side at its midpoint. This property shows that the median effectively bisects the side, as it divides it into two equal segments. Thus, by the definition and properties of medians, we can conclude that they bisect the sides of the triangle.
What is a median median line?
It is the line joining the midpoints of two sides of a polygon - usually a triangle. This line will be parallel to the third side. The three median-median lines will divide any triangle into 4 congruent triangles that are similar to the original.It is the line joining the midpoints of two sides of a polygon - usually a triangle. This line will be parallel to the third side. The three median-median lines will divide any triangle into 4 congruent triangles that are similar to the original.It is the line joining the midpoints of two sides of a polygon - usually a triangle. This line will be parallel to the third side. The three median-median lines will divide any triangle into 4 congruent triangles that are similar to the original.It is the line joining the midpoints of two sides of a polygon - usually a triangle. This line will be parallel to the third side. The three median-median lines will divide any triangle into 4 congruent triangles that are similar to the original.
In an isosceles triangle does the median to the base bisect the vertex angle?
In the diagram, ABC is an isoscels triangle with the congruent sides and , and is the median drawn to the base . We know that ∠A ≅ ∠C, because the base angles of an isosceles triangle are congruent; we also know that ≅ , by definition of an isosceles triangle. A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. That means ≅ . This proves that ΔABD ≅ ΔCBD. Since corresponding parts of congruent triangles are congruent, that means ∠ABD≅ ∠CBD. Since the median is the common side of these adjacent angles, in fact bisects the vertex angle of the isosceles triangle.
If the median to a side of a triangle is also an altitude to that side then the triangle is isosceles How do you write this Proof?
Let the triangle be ABC and suppose the median AD is also an altitude.AD is a median, therefore BD = CDAD is an altitude, therefore angle ADB = angle ADC = 90 degreesThen, in triangles ABD and ACD,AD is common,angle ADB = angle ADCand BD = CDTherefore the two triangles are congruent (SAS).And therefore AB = AC, that is, the triangle is isosceles.
The median to the hypotenuse of a right triangle divided the triangle into two triangles that are both what?
Isosceles.
What ratio does a median divide two equilateral triangle?
A median divides any triangle in half.
In an isosceles triangle what are the altitude and media?
In an isosceles triangle, the altitude from the vertex angle to the base bisects the base and is also the median, as it divides the triangle into two congruent right triangles. This altitude is perpendicular to the base, creating two equal segments. Consequently, in an isosceles triangle, the altitude, median, and angle bisector from the vertex angle to the base are all the same line segment.
Which segment always divides a triangle into two triangles of equal areas?
median
How is the altitude and a median of a triangle the same?
they are the same because the triangles side is equal
What triangle shows medians bisect the sides of a triangle?
Medians bisect the sides of ALL triangles. That is what a median is, by definition!
Can the median of an equilateral triangle be longer than its altitude?
For the equilateral triangle in Euclidean space(i.e, the triangles you see in general) median is the same as its altitude. So, both are of equal length.
How does the centroid divide each median in a triangle?
2/3 of the median is between the centroid and the vertex, 1/3 between the centroid and the side.
What is the difference between altitude angle bisector and median?
The altitude is the segment from an angle of a triangle to the side opposite of the angle which is intersected perpendicularly by the altitude., the angle bisector cuts an angle into two congruent angles, and a median forms two congruent line segments.
