Draw an isoscale triangle . Draw all of its medians and altitudes . write your observations about their points of concurrence.
Answers
Answer:
Step-by-step explanation:
Answer :
i. Draw an isosceles triangle and name it as PQR.
An isosceles triangle is that triangle whose base is the side which is not equal to the other two sides or An isosceles triangle is a triangle which has two equal sides.
ii. Now, mark the mid-point i.e., A, B, C, of all the sides of the triangle and join it with the opposite vertex i.e., P, Q, R. The line segment i.e., PA, QB, RC hence found are the median of the triangle.
iii. Mark the point of concurrence as 'O'.
iv. Again, draw perpendicular line segment from each vertex.
v. Mark the point of concurrence X.
Here we see that both the point of concurrence of medians and altitudes coincides.
In the case of isosceles triangle, the two sides that are equal meet at a vertex, that lies directly above the midpoint of the base. Because of this, the altitude that runs from P to the base intersects the base at its midpoint, making it the median from P to the base as well, which is same for the other two sides also.
Therefore, in an isosceles triangle, the altitude and median are the same line segment, which is shown through the bold line in the above-given figure.