Home
Class 9
MATHS
In Fig. 6.16, if x+y=w+z, then prove tha...

In Fig. 6.16, if `x+y=w+z`, then prove that AOB is a line.

Text Solution

Verified by Experts

`angleBOC+angleCOA+angleAOD+angleDOB=360^o`
x+y+z+w=`360^0`
(x+y)+(w+z)=`360^o`
(x+y)=(w+z)=`180^o`non common arms of angles forms a line
putting this value in equation (1)
2(x+y)=`360^o`
(x+y)=`180^o`
so, AOB is a line.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LINES AND ANGLES

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|8 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NCERT ENGLISH|Exercise Exercise 4.1|2 Videos

  • NCERT THEOREMS

    NCERT ENGLISH|Exercise THEOREM 10.12|1 Videos

Similar Questions

Explore conceptually related problems

In Figure, if x+y=w+z , then prove that A O B is a line.

In Figure, if x+y=w+z , then prove that A O B is a line

If z=z_0+A( bar z -( bar z _0)), w h e r eA is a constant, then prove that locus of z is a straight line.

In the adjoining figure, find the values of x and y, Given that AOB is a straight line.

If omega!=1 is a cube root of unity and x+y+z!=0, then prove that |[x/(1+omega), y/(omega+omega^2),z/(omega^2+1)],[y/(omega+omega^2),z/(omega^2+1),x/(1+omega)],[(z)/(omega^2+1),x/(1+omega),y/(omega+omega^2)]|=0 if x=y=z

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

Find the value of x if AOB is a straight line

In given fig., if (x)/(3)=(y)/(4)=(z)/(5) , then calculate the values of x,y and z.

If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus of omega is equivalent to |z-2|=|z+2|

If z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is purely real.

Home
Profile