Home
Class 9
MATHS
In Fig. , the side QR of △ PQR is prod...

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`.

Text Solution

Verified by Experts

`In/_ PQR`
`anglePRS=anglePQR+angleQPR`(exterior angle of triangle)
`1/2 anglePRS=1/2anglePQR+1/2angleQPR`
`angleTRS=angleTQS+1/2angleQPR-(1)`
`In/_QTS`
`angleTRS=angleTQR+angleQTR-(2)`
`angleTQS+angleQTR=angleTQS+1/2angleQPR`
`angleQTR=1/2angleQPR`
Promotional Banner

Topper's Solved these Questions

  • LINES AND ANGLES

    NCERT ENGLISH|Exercise EXERCISE 6.2|6 Videos

  • 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 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. 6.15, /_P Q R=/_P R Q , then prove that /_P Q S=/_P R T .

In Figure, /_P Q R=\ /_P R Q , then prove that /_P Q S=\ /_P R Tdot

In Fig. 6.39, sides QP and RQ of DeltaP Q R are produced to point S and T respectively. If /_S P R=135^@ and /_P Q T=110^@ , find /_P R Q.

In Figure, P Q > P R. Q S\ a n d\ R S are the bisectors of /_ Q and /_R respectively. Prove that S Q > S R .

In Fig. if S T || Q R . Find P S

sides Q P and R Q of P Q R are produced to point S and T respectively. If /_S P R=135^0 and /_P Q T=110^0, find /_P R Qdot

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 figure PS is the bisector of /_Q P R of DeltaP Q R . Prove that (Q S)/(S R)=(P Q)/(P R) .

In Figure, side Q P\ a n d\ R Q of P Q R are produced to point S\ a n d\ T respectively. If /_S P R=135^0a n d\ /_P Q T=110^@ , find /_P R Q