If we join a vertex to a point on the opposite side which divides that side in the ratio 1:1, then what is the special name of that line segment?
a. Median
b. Angle bisector
c. Altitude
d. Hypotenuse

Solution:

Given, we join a vertex to a point on the opposite side

The line segment divides the side in the ratio 1 : 1

We have to find the special name of the line segment.

The line segment joining a vertex of a triangle to the midpoint of its opposite side is called a median of the triangle.

From the properties of Median of Triangle,

(i) The median bisects the opposite side, dividing it into two equal parts.

(ii) The median of a triangle further divides the triangle into two triangles having the same area.

(iii) Every triangle has 3 medians, one from each vertex. The point of concurrency of 3 medians forms the centroid of the triangle.

(iv) Each median of a triangle divides the triangle into two smaller triangles that have equal areas. In fact, the 3 medians divide the triangle into 6 smaller triangles of equal area.

Considering triangle ABC,

From the above property,

The altitude AD divides BC into two equal parts.

BD / DC = 1/1

So, BD : DC = 1 : 1

Therefore, the special name of the line segment is median.

✦ Try This: In ∆ABC, if ∠A = 90°, and ∠B = 60°, then the exterior angle formed by producing BC is equal to

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 33

If we join a vertex to a point on the opposite side which divides that side in the ratio 1:1, then what is the special name of that line segment? (a) Median (b) Angle bisector (c) Altitude (d) Hypotenuse

Summary:

If we join a vertex to a point on the opposite side which divides that side in the ratio 1:1, then the special name of that line segment is median

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