Question

In fig. 3.22, seg AB $\cong$ seg PB, sec BC $\cong$ seg BQ $\angle$ABP $\cong$ $\angle$CBQ show that $△$ABC $\cong$$△$ PBQ also show seg AC $\cong$ seg PQ

Answer 1

Given : seg AB $\cong$ seg PB
seg BC $\cong$ seg BQ
$\angle$ABP $\cong$ $\angle$CBQ
Adding $\angle$PBC on both the sides, we get:
$\angle$ABP + $\angle$PBC $\cong$ $\angle$CBQ + $\angle$PBC
Or, $\angle$ABC $\cong$ $\angle$PBQ … (1)
In $△$ABC and $△$PBQ,
seg AB $\cong$ seg PB (given)
$\angle$ABC $\cong$ $\angle$PBQ {from equation (1)}
seg BC $\cong$ seg BQ (given)
So,$△$ABC $\cong$ $△$PBQ (SAS congruency test)
Hence, seg AC $\cong$ seg PQ (c.s.c.t)