Question

An arc through P and Q and two arcs intersecting at R have been drawn. One arc at R has been drawn from P and the other has been drawn from Q using the same compass setting. QR⎯⎯⎯⎯⎯ and PR⎯⎯⎯⎯⎯ have also been drawn.
Determine the correct justification needed for each statement to prove ∠PAR≅∠QAR.

Answer 1

$\\ \sf\longmapsto AR\cong AR(Common\: side)$

• AR is present in both triangles so it's common

$\\ \sf\longmapsto ∆ARP\cong ∆ARQ(SSS congruence)$

• SSS stands for Side Side Side
• As both triangles are equal so so respective angles are also equal

$\\ \sf\longmapsto$

Answer 2

Key points :-

☏︎ To prove these angle congruent we will prove △ARP≅△ARQ.

☏︎ After this, ∠PAR ≅ ∠QAR by CPCT.

☏︎ The full form of CPCT is corresponding parts of congruent triangles.

☏︎ The full form of SSS is Side-Side-Side.

$\purple{ \rule{300pt}{3pt}}$

⚘ Refer to the attachment for solution!!~