Home
Class 9
MATHS
In Fig. 9.24, ABC and ABD are two trian...

In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that ``

Text Solution

Verified by Experts

Given, ABC and ABD are two triangle on the same base AB.
The line segment CD is bisected by AB at O. `( .: OC = OD)`
In `DeltaACD`, we have
`OC= OD` (given)
`:. AO` is the median.
Since, the median divides a triangle in two triangles of equal areas.
`:. ar(DeltaAOC) = ar(DeltaAOD)`...(1)
Similarly, in `DeltaBCD, " " ar(DeltaBOC) = ar(DeltaBOD)`...(2)
On adding (1) and (2), we get
`ar(DeltaAOC) + ar(DeltaBOC) = ar(DeltaAOD) + ar(DeltaBOD)`
`rArr ar(DeltaABC) = ar(ABD)`
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|34 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (very Short Answer Questions)|10 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (long Answer Question)|5 Videos

  • CIRCLE

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (long Answer Questions )|5 Videos

Similar Questions

Explore conceptually related problems

In Figure, A B C\ a n d\ ABD are two triangles on the base A B . If line segment C D is bisected by A B\ a t\ O , show that a r\ (/_\ A B C)=a r\ (\ /_\ A B D)

In figure ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (a r(A B C))/(a r(D B C))=(A O)/(D O) .

ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that /_A B D\ =/_A C D

ABC and DBC are two triangle on the same base BC such that A and D lie on the opposite sides of BC,AB=AC and DB =DC ,Show that AD is the perpedicular bisector of BC.

In the given figure, AB||CD . The line segments BC and AD intersect at O. Show that : z=x+y .

Triangles ABC and DBC are two isosceles triangles on the same base BC and their vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that: AP bisects angle BAC and BDC.

In Fig. 6.28, find the values of x and y and then show that AB || CD.

AB is a line segment and M is its mid point. Three semi circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle with radius r unit is drawn so that it touches all thethree semi- circles. Show that AB=6xxr

In the figure, O is the center of the circle and BO is the bisector of /_ ABC show that AB=BC

The given figure shows two isosceles triangles ABC and DBC with common base BC. AD is extended to intersect BC at point P. Show that: Delta ABD = Delta ACD (ii) Delta ABP = Delta ACP (iii) AP bisects angle BDC (iv) AP is perpendicular bisector of BC.