Ex.6.1 Q3 Lines and Angles Solution - NCERT Maths Class 9

Go back to  'Ex.6.1'

Question

In the given figure, \(\angle PQR = \angle PRQ\) then prove that \(\angle PQS = \angle PRT.\)

 

 Video Solution
Lines And Angles
Ex 6.1 | Question 3

Text Solution

What is known?

\(\angle PQR = \angle PRQ\)

What is unknown?

To prove \(\angle PQS = \angle PRT\)

Reasoning:

If a ray stands on a line, then the sum of adjacent angles formed is \(180^ {\circ}.\)

steps:

Let \(\angle PQR= \angle PRQ = a\)

Let \(\angle PQS = b \) and \(\angle PRT = c \)

Line \(ST \) and \(PQ\) intersect at point \(Q\), then the sum of adjacent angles \(\angle PQS\) and \(\angle PQR\) is \(180^ {\circ}.\)

\(\begin{align} \angle PQS + \angle PQR & = 180 ^ { \circ } \\ b + a & = 180 ^ { \circ } \\ b & = 180 ^ { \circ } - a\ldots . ( 1 ) \end{align}\)

Line \(ST\) and \(PR\) intersect at point \(R\), then the sum of adjacent angles \(\angle PRQ\) and \(\angle PRT \) is \(180^ {\circ}.\)

\(\begin{align} \angle PRQ + \angle PRT & = 180 ^ { \circ } \\ a + c & = 180 ^ { \circ } \\ c & = 180 ^ { \circ } - a\ldots . ( 2 ) \end{align}\)

From equations (\(1\)) and (\(2\)), it is clear that \(b = c.\)

Hence \(\angle PQS = \angle PRT\) is proved.

 Video Solution
Lines And Angles
Ex 6.1 | Question 3
  
Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school