P is the mid-point of side B C of a p...

`P` is the mid-point of side `B C` of a parallelogram `A B C D` such that `/_B A P=/_D A Pdot` If `A D=10 c m ,\ ` then `C D=` 5cm (b) 6cm (c) 8cm (d) 10cm

Text Solution

Verified by Experts

Given: ABCD is a parallelogram
P is mid point of side BC
`angleBAP=angleDAP`
AD=10cm
`AD|\|BC`
`angleDAP=angleAPB`(alternate angles)
`angleDAP=angleBAP`
`AB=BP` (side opposite to equal angles)
...

Topper's Solved these Questions

PROBABILITY
RD SHARMA|Exercise All Questions|67 Videos
RATIONALISATION
RD SHARMA|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

A B C P Q R such that a r( A B C)=4a r( P Q R)dot If B C=12 c m , then Q R= (a) 9cm (b) 10cm (c) 6cm (d) 8cm

In Figure, A B C D is a parallelogram. If A B=12\ c m ,\ \ A E=7. 5\ c m ,\ C F=15\ c m , then A D= 3 cm (b) 6 cm (c) 8 cm (d) 10.5 cm

In A B C ,\ E is the mid-point of median A D such that B E produced meets A C\ at Fdot If A C=10. 5\ C M , then A F= 3cm (b) 3.5cm (c) 2.5cm (d) 5cm

P is the mid-point of side A B of a parallelogram A B C D . A line through B parallel to P D meets D C at Q\ a n d\ A D produced at Rdot Prove that: A R=2B C (ii) B R=2\ B Q

In a A B C , A D is the bisector of /_B A C . If A B=8c m , B D=6c m and D C=3c m . Find A C 4c m (b) 6c m (c) 3c m (d) 8c m

A B C D is a trapezium in which A B||D C , M\ a n d\ N are the mid-points of A D\ a n d\ B C respectively. If A B=12 C M ,\ M N=14 C M ,\ then C D= 10cm (b) 12cm (c) 14cm (d) 16cm

A B C D is a trapezium in which A B D Cdot If a r( A B D)=24\ c m^2a n d\ A B=8\ c m , then height of A B C is 3 cm (b) 4 cm (c) 6 cm (d) 8 cm

In Fig.42, A B C D is a parallelogram in which A D=21\ c m , D H=18\ c m and D K=27\ c mdot The length of side A B is 63 cm (b) 63.5 cm 31.5 cm (d) 31 cm

If A B C D E F such that D E=3c m , E F=2c m , D F=2. 5 c m , B C=4c m , then perimeter of A B C is (a) 18cm (b) 20cm (c) 12cm (d) 15cm

In Figure, P is a point in the interior of a parallelogram A B C D . Show that a r( A P B)+a r( P C D)=1/2a r(^(gm)A B C D) a R(A P D)+a r( P B C)=a r( A P B)+a r( P C D)

RD SHARMA-QUADRILATERALS-All Questions

The figure formed by joining the mid-point of the adjacent sides of...
Text Solution
|
Find the measure of all the angles of a parallelogram, if one angle is...
Text Solution
|
In a parallelogram A B C D , if /D A B=75^@ and /D B C=60^@, then /B D...
Text Solution
|
In a parallelogram A B C D , if /D A B=75^@and /D B C=60^@, then /B D ...
Text Solution
|
A B C D is a parallelogram and E and F are the centroids of triangle...
Text Solution
|
A B C D is a parallelogram, M is the mid-point of B D and B M bisects ...
Text Solution
|
A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d...
Text Solution
|
If an angle of a parallelogram is two-third of its adjacent angle, f...
Text Solution
|
If the degree measures of the angles of quadrilateral are 4x ,\ 7x ...
Text Solution
|
In a quadrilateral A B C D ,\ /A+/C is 2 times /B+/Ddot If /A=140^@\ a...
Text Solution
|
If the diagonals of a rhombus are 18 c m\ a n d\ 24 c m respectively...
Text Solution
|
The diagonals A C\ a n d\ B D of a rectangle A B C D intersect each ot...
Text Solution
|
A B C D is a parallelogram in which diagonal A C\ bisects /B A Ddot...
Text Solution
|
In a rhombus A B C D , if /A C B=40^@, then /A D B=(a) 70^@ (b) 45...
Text Solution
|
In A B C ,\ /A=30^@,\ /B=40^@a n d\ /C=110^@dot The angles of the t...
Text Solution
|
The diagonals of a parallelogram A B C D intersect at O . If /B O C=...
Text Solution
|
A B C D is a trapezium in which A B|\|D C , M\ a n d\ N are the mid-...
Text Solution
|
Diagonals of a quadrilateral A B C D bisect each other. If /A=45^@, ...
Text Solution
|
P is the mid-point of side B C of a parallelogram A B C D such that...
Text Solution
|
In A B C ,\ E is the mid-point of median A D such that B E produce...
Text Solution
|