in an isosceles triangle
Because it's perpencicular to its apex
Only one line of symmetry, it is the line that contains the median of the isosceles triangle (that passes through the vertex and perpendicular to the base).
Divide the base in half and draw the median from the apex. This median is also the altitude and so its length is the required height. Also, since it is the altitude, it forms a right angled triangle. Using Pythagoras on this triangle, the height is 9*sqrt(3)/2.
It is a triangle whose interior angles are 45, 45 and 90 degrees
in an isosceles triangle
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.
Because it's perpencicular to its apex
Not always. 1. The median to the base of an isosceles triangle bisects the vertex angle. 2. When the triangle is an equilateral triangle, then the medians bisect the interior angles of the triangle.
It is not possible to answer the question since it is hopelessly underspecified and does not provide enough information.what information about the triangle is known? All three side lengths, base angle and base side, base angle and leg, apex angle and base, apex angle and leg? These could influence the form of the answer.is the information about the triangle in terms of analytical geometry (coordinates of points and equations of lines) or in some other form?which median? The median from the apex or one of the isosceles medians?what aspect of the median is the formula supposed to give? Its length, equation?
Only one line of symmetry, it is the line that contains the median of the isosceles triangle (that passes through the vertex and perpendicular to the base).
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.
No. It need not be the base angles that are equal, it can be one of the base angles and the top angle (if the triangle is tipped over). Also, the base angle are equal in an equilateral triangle - although an equilateral triangle is a special kind of isosceles triangle.
The median of an isosceles triangle from its apex is also the perpendicular bisector of the base. This line divides the triangle into two congruent right angled triangles whose hypotenuse is 3 feet and whose apical angle is 35/2 = 17.5 degrees. If the base of the original triangle was 2b cm then sin(17.5) = b/3 so that b = 3*sin(17.5) = 0.9cm so that the base was 2b = 1.8 feet Alternatively, you could use the sine rule on the triangle:
Divide the base in half and draw the median from the apex. This median is also the altitude and so its length is the required height. Also, since it is the altitude, it forms a right angled triangle. Using Pythagoras on this triangle, the height is 9*sqrt(3)/2.
Yes. If you have an isosceles triangle standing up on the unequal side, thenthe line segment from the top vertex perpendicular to the base is all of these.
It is a triangle whose interior angles are 45, 45 and 90 degrees