Statement 2: The altitude of ?B to AC is a median in triangle ABC. But we have no idea about the measure of angle A. This means triangle ABC must be an isosceles triangle such that AB = AC. Solution: We are given a triangle ABC but we don’t know what kind of a triangle it is. Statement 2: The altitude of B to AC is a median in triangle ABC. Statement 1: The bisector of ?A is a median in triangle ABC. Let’s take a quick question on these concepts: A median which is an altitude implies the triangle is isosceles which implies it is also the angle bisector.
– Can we have a median from vertex A which is perpendicular to BC but does not bisect the angle A? No. Angle bisector which is also a median implies isosceles triangle which implies it is also the altitude. – Can we have an angle bisector which is also a median which is not perpendicular? No. – Should an angle bisector in a triangle which is also a median be perpendicular to the opposite side? Yes. Try to prove all these properties on your own. In an equilateral triangle, each altitude, median and angle bisector drawn from the same vertex, overlap. – If median drawn from vertex A is also the angle bisector, the triangle is isosceles such that AB = AC and BC is the base. Hence this altitude is also the angle bisector. – If altitude drawn from vertex A is also the median, the triangle is isosceles such that AB = AC and BC is the base. Hence this angle bisector is also the altitude. – If angle bisector of vertex A is also the median, the triangle is isosceles such that AB = AC and BC is the base. – the bisector of the angle opposite to the base is the altitude and the median. – the median drawn to the base is the altitude and the angle bisector – the altitude drawn to the base is the median and the angle bisector In an isosceles triangle (where base is the side which is not equal to any other side): We will now give you some properties which can be very useful. But in special triangles such as isosceles and equilateral, they can overlap. Usually, medians, angle bisectors and altitudes drawn from the same vertex of a triangle are different line segments. Median – A line segment joining a vertex of a triangle with the mid-point of the opposite side.Īngle Bisector – A line segment joining a vertex of a triangle with the opposite side such that the angle at the vertex is split into two equal parts.Īltitude – A line segment joining a vertex of a triangle with the opposite side such that the segment is perpendicular to the opposite side. Lets start by defining them: median, angle bisector and altitude.
0 kommentar(er)
