In Figure, if A B||D C\ a n d\ P is the ...

In Figure, if `A B||D C\ a n d\ P` is the mid-point `B D ,` prove that `P` is also the midpoint of `A C`

Text Solution

AI Generated Solution

Topper's Solved these Questions

CIRCLE
RD SHARMA ENGLISH|Exercise All Questions|306 Videos
CONSTRUCTION
RD SHARMA ENGLISH|Exercise All Questions|40 Videos

Similar Questions

Explore conceptually related problems

In Figure, l||m and M is the mid-point of the line segment A B . Prove that M is also the mid-pooint of any line segment C D having its end-points on l\ a n d\ m respectively.

A B C is a triangle right angled at B ; a n d\ P is the mid-point of A C . Prove that: P Q\ _|_A B (ii) Q is the mid point of A B P B=P A=1/2A C

In Figure, if A B=A C\ a n d\ /_B=/_Cdot Prove that B Q=C P

In Figure, A C > A B\ a n d\ D is the point on A C such that A B=A Ddot Prove that B C > C D

In Figure, A B C D is a parallelogram and /_D A B=60^@ . If the bisectors A P\ a n d\ B P of angles A\ a n d\ B respectively, meet at P on C D , prove that P is the mid-point of C D .

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A C . If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C .

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

In Figure, line segment A B is parallel to another line segment C D . O is the mid-point of A D . Show that: (i) AOB~= D O C (ii) O is also the mid-point of B Cdot

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A P . Prove that: a r\ ( triangle P B Q)=\ a r\ (triangle \ A R C)

RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions

A B is a line segment. A X\ a n d\ B Y are two equal line segments d...
Text Solution
|
l\ a n d\ m are two parallel lines intersected by another pair of p...
Text Solution
|
In Figure, if A B||D C\ a n d\ P is the mid-point B D , prove that P i...
Text Solution
|
In Figure, /B C D=/A D C\ a n d\ /A C B=/B D Adot Prove that A D=B C\ ...
Text Solution
|
In two right triangles, one side and an acute angle of one triangle...
Text Solution
|
In Figure, A C=B C ,\ /D C A=/E C B\ a n d\ /D B C=E A Cdot Prove that...
Text Solution
|
In Figure, it is given that R T=T S ,\ /1=2/2\ a n d\ /4=2/3 . Prov...
Text Solution
|
Two lines A B\ a n d\ C D intersect at O such that B C is equal and pa...
Text Solution
|
B D\ a n d\ C E are bisectors of /B\ a n d\ /C of an isosceles A B C ...
Text Solution
|
In Figure, A B=A C\ a n d\ D B=D Cdot\ Prove that /A B D=/A C D
Text Solution
|
\ ABC is an isosceles triangle with A B=A C. Side B A is produced to...
Text Solution
|
In Figure, A B=A CdotB E\ a n d\ C F are respectively the bisectors ...
Text Solution
|
If A B C is an isosceles triangle with A B=A Cdot Prove that the ...
Text Solution
|
If the altitudes from two vertices of a triangle to the opposite si...
Text Solution
|
In Figure, it is given that /A=/C\ a n d\ A B=B Cdot Prove that A ...
Text Solution
|
A D\ a n d\ B C are equal perpendiculars to a line segment A B . Sh...
Text Solution
|
In A B C ,\ A B=A C , and the bisectors of angles B\ a n d\ C inte...
Text Solution
|
In Figure, it is given that A B=E F ,\ B C=D E ,\ A B\ |B D\ a n d\ ...
Text Solution
|
In Figure, it is given that A B=B C\ a n d\ A D=E C. Prove that (i) ...
Text Solution
|
In Figure, l||m and M is the mid-point of the line segment A B . Pr...
Text Solution
|