The median of a triangle divides it into two
a. triangles of equal area
b. congruent triangles
c. right triangles
d. isosceles triangles

Solution:

Consider a triangle ABC

Construct AP perpendicular to BC

As D is the midpoint of BC

BD = DC

Let us multiply both sides by AP

BD × AP = DC × AP

Here

1/2 × BD × AP = 1/2 × DC × AP

ar (Δ ABD) = ar (Δ ACD)

Median of a triangle divides it into two triangles of equal area.

Therefore, the median divides it into two triangles of equal area.

✦ Try This: The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 17 cm and 20 cm is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 9

NCERT Exemplar Class 9 Maths Exercise 9.1 Problem 1

The median of a triangle divides it into two a. triangles of equal area, b. congruent triangles, c. right triangles, d. isosceles triangles

Summary:

A line segment, joining a vertex to the mid-point of the side opposite to that vertex, is called the median of a triangle. The median of a triangle divides it into two triangles of equal area

☛ Related Questions:

• In which of the following figures (Fig. 9.3), you find two polygons on the same base and between the . . . .
• The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and . . . .
• In Fig. 9.4, the area of parallelogram ABCD is : a. AB × BM, b. BC × BN, c. DC × DL, d. AD × DL