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The theorem is only true if the base is the side of different length.
To see this consider the right angled isosceles triangle with sides 1, 1 and √2. If one of the sides of length 1 is the base, the height is obviously the other side of length 1, but it clearly does not meet the base at its mid-point to make it a median.
So with an isosceles triangle ABC with sides AB & AC equal, angles ABC & ACB equal and side BC the base, we need to prove that the point X where the height (AX) meets BC is such that BX = CX.
Consider triangles AXB and AXC.
- Angle AXB is a right angle, as is AXC (since AX is a height of triangle ABC).
- Side AB is the hypotenuse of triangle AXB; AC is the hypotenuse of triangle AXC; they are known to be equal (from isosceles triangle ABC)
- Side AX is common to both triangles
Thus triangles AXB and AXC are congruent since we have a Right-angle, Hypotenuse, Side match.
Thus XB must be the same length as XC, that is X is the mid-point of BC.
As X is the mid-point of BC, AX is the median.
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What is the median of an isosceles triangle is the same segment in the triangle?
Altitude APEXX
If is both the altitude and median of triangle ABC then triangle ABC is?
It is isosceles.
If is both the altitude and median of triangle ABC then triangle ABC is .?
It is isosceles.
The median to the hypotenuse of a right triangle divided the triangle into two triangles that are both what?
Isosceles.
In an isosceles triangle the altitude and median are?
B. The same segment. ~Ãpex
If a median of a triangle is also an altitude of a triangle then is the triangle isosceles?
Yes
Can the altitude from the vertex angle of an isosceles triangle be the median?
If the triangle is really isosceles, and it's not lying on one of the equal sides, then the altitude is always a median.
What is the median of an isosceles triangle is the same segment in the triangle?
Altitude APEXX
If is both the altitude and median of triangle ABC then triangle ABC is?
It is isosceles.
If is both the altitude and median of triangle ABC then triangle ABC is .?
It is isosceles.
When does the median of the triangle bisect the base at 90 degree?
in an isosceles triangle
The median to the hypotenuse of a right triangle divided the triangle into two triangles that are both what?
Isosceles.
What triangle has an altitude which is also a median and angle bisector?
An isosceles or an equilateral triangle perhaps?
How do you find the perpendicular height of a isoceles triangle?
You can find it by using the Pythagorean theorem if you know the side and the base of triangle. In an isosceles triangle the median is also the altitude. The formula is: (The measure of the side length)^2 - (The measure of the one half of the base length )^2 = (The measure of the altitude)^2. Find the square root of the result that you'll have the measure of the altitude.
In an isosceles triangle the altitude and median are?
B. The same segment. ~Ãpex
Can the median and altitude of a triangle meet in the same line segment?
Yes, if the triangle is isosceles or equilateral.
What median of an isosceles triangle is the same segment in the triangle as the leg bisector hypotenuse altitude?
It is the median which divides the side which is not one of the equal sides.
