Yes, it is very much possible that the median and altitude of an isosceles triangle is the same. for example, The given triangle has the same median and altitude.
i) The triangle ABC
Based on Side: In Triangle ABC, Since two sides (BC and AC ) are equal (= 8 cm ) The given triangle is an isosceles triangle.
Based on Angle: In Triangle ABC, Since all the triangles are less than 90 degrees, So the given triangle is Acute angled triangle.
ii) The Triangle PQR
Based on Side: In Triangle PQR, All the sides are different so, The given triangle is a...
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex.
Yes, the altitude and median can be the same in a triangle. for example, consider an equilateral triangle, the median which divides the side in equal is also perpendicular to the side and hence the altitude and the median is the same.
No, the altitude of a triangle might lie outside the triangle. for example in the obtuse-angled triangle, we have to extend the base side for making altitude angle.
Every triangle has three bases (any of its sides) and three altitudes (heights). Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side.
As we know that in a triangle, the exterior angle is equal to the sum of opposite interior angles.
So,
Exterior Angle = + .
=
Hence the measure of the exterior is .
As we know that in a triangle, the exterior angle is equal to the sum of opposite interior angles.
So,
According to the question,
Hence the other interior angle is .
No, the exterior angle of a triangle cannot be a straight angle because if the exterior angle is straight then there won't be any triangle left that would be a straight line. (imagine it visually).
(i) a right angle
When the exterior angle is , the sum of opposite internal angles is
(ii) an obtuse angle
When the exterior angle is the obtuse angle, the opposite interior angles can be both acute, one right and one acute and one obtuse and one acute.
(iii) an acute angle?
When the exterior angle is an acute angle, both the internal angle has to be acute angles.
Let the angles of the triangles be
So,
As we know the sum of internal angles of a triangle is 180. so,
Hence the angles of the triangles are .
On the Basis of sides, the triangle is isosceles triangle as two sides of the triangle are equal.
On the Basis of angle, the triangle is Right-Angled Triangle as it has one angle equal to 90 degrees.