The median of a triangle divides it into two
a. triangles of equal area
b. congruent triangles
c. right triangles
d. isosceles triangles
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
1/2 × BD × AP = 1/2 × DC × AP
ar (Δ ABD) = ar (Δ ACD)
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
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