Advertisements
Advertisements
Question
If AD is a median of a triangle ABC, then prove that triangles ADB and ADC are equal in
area. If G is the mid-point of median AD, prove that ar (Δ BGC) = 2 ar (Δ AGC).
Advertisements
Solution
Draw AM ⊥ BC
Since, AD is the median of ΔABC
∴ BD = DC
⇒ BD = AM = DC × AM
⇒ ` 1/2 (BD xx AM ) = 1/2 ( DC xx AM)`
⇒ ar (Δ ABC) = ar (Δ ACD) ........ (1)
In ΔBGC , GDis the median
∴ ar (BGD) = area (OGD) ......... (2)
In ΔACD , CG is the median
∴ area (AGC) = area (Δ CGD) ......... (3)
From (1) and (2) , we have
Area (ΔBGD) = ar (Δ AGC)
But, ar (ΔBGC) = 2ar (BGD)
∴ ar (BGC ) = 2ar (Δ AGC)
APPEARS IN
RELATED QUESTIONS
ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O
intersects AB at P and DC at Q. Prove that ar (Δ POA) = ar (Δ QOC).
If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (ΔABC) : ar (ΔBDE).
Let ABC be a triangle of area 24 sq. units and PQR be the triangle formed by the mid-points of the sides of Δ ABC. Then the area of ΔPQR is
ABCD is a parallelogram. P is any point on CD. If ar (ΔDPA) = 15 cm2 and ar (ΔAPC) = 20 cm2, then ar (ΔAPB) =
A, B, C, D are mid-points of sides of parallelogram PQRS. If ar (PQRS) = 36 cm2, then ar (ABCD) =
ABCD is a trapezium in which AB || DC. If ar (ΔABD) = 24 cm2 and AB = 8 cm, then height of ΔABC is
Measure the length of the floor of your classroom in meters. Also, measure the width.
- What is the area of the floor of your classroom in square metres?
If each square on this page is equal to 1 square meter of land, how much land will each of her children get? ________ square m
The King was very happy with carpenters Cheggu and Anar. They had made a very big and beautiful bed for him. So as gifts the king wanted to give some land to Cheggu, and some gold to Anar. Cheggu was happy. He took 100 meters of wire and tried to make different rectangles.
He made a 10 m × 40 m rectangle. Its area was 400 square meters. So he next made a 30 m × 20 m rectangle.
- What other rectangles can he make with 100 meters of wire? Discuss which of these rectangles will have the biggest area.
Find the area of the following figure by counting squares:
