Question

Angle pqr equal angle prq then prove that angle pqs equal angle prt

Answer 1

Given,


∠PQR = ∠PRQ


To prove:
∠PQS = ∠PRT


Proof:


∠PQR +∠PQS =180° (by Linear Pair axiom)


∠PQS =180°– ∠PQR — (i)

∠PRQ +∠PRT = 180° (by Linear Pair axiom)


∠PRT = 180° – ∠PRQ


∠PRQ=180°– ∠PQR — (ii)

[∠PQR = ∠PRQ]


From (i) and (ii)


∠PQS = ∠PRT = 180°– ∠PQR


∠PQS = ∠PRT


The required axioms for this probelm are given below

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.



Axiom- 1

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.



Axiom-2

If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.



The two axioms given above together are called the linear pair axioms.