Home
Class 9
MATHS
In Fig. 6.17, POQ is a line. Ray OR is ...

In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that `/_R O S=1/2(/_Q O S-/_P O S)dot`

Text Solution

Verified by Experts

`anglePOR+angleROQ=180^o`
`angleROP=angleROQ=90^o`
`angleSOQ=anfleROS+angleROQ`
`angleROS=angleSOQ-angleROQ -(1)`
`angleROP=angleROS+anglePOS
`angleROS=angleROP-anglePOS-(2)
adding 1 and 2
`angleROS+angleROS=angleSOQ+angleROP-angleROQ-anglePOS` ...
Promotional Banner

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, P O Q is a line. Ray O R is perpendicular to line P Q . O S is another ray lying between rays O P\ a n d\ O R . Prove that /_R O S=1/2(/_Q O S-/_P O S)

In figure POQ is a line. Raw Oris perpendicular to line PQ .OS is another ray lying between rays OP and OR. Prove that angleROS(1)/(2) (angleQOS-anglePOS)i.e., angle1=(1)/(2)(angle2-angle3)

In Figure, P O S is a line, find x

In Fig.29, P O S is a line, find xdot

If PS is the bisector of /_Q P R and P T_|_Q R . Show that /_T P S=1/2(/_Q-/_R)dot

In Fig. 6.44, the side QR of PQR is produced to a point S. If the bisectors of /_P Q R"\ "a n d/_P R S meet at point T, then prove that /_Q T R=1/2/_Q P R .

In Fig. 6.10, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of /_P O S and /_S O Q , respectively. If /_P O S=x , find /_R O T .

In Fig. , the side QR of △ PQR is produced to a point S. If the bisectors of /_P Q R and /_P R S meet at point T, then prove that /_Q T R=1/2/_Q P R .

In Fig. 6.11, OP, OQ, OR and OS are four rays. Prove that /_P O Q+/_Q O R+/_S O R+/_P O S=360o

In Fig. 6.11, OP, OQ, OR and OS are four rays. Prove that /_P O Q+/_Q O R+/_S O R+/_P O S=360o