Question

In triangle ABC and triangle PQR, AB=PQ, BC=QR;
CB=RQ are extended to X and Y respectively. angle ASX = angle PQY. Prove that triangle ABC is congruent to triangle PQR.

Answer 1

@dpasingh

Answer 2

CORRECTION: I feel that there should be Angle ABx instead of angle ASX.

Answer 3

Now in \[\triangle AXC - and - \triangle PYR\]
We have
\[\angle ABX + \angle ABC = 180^0--[linear -pair - angles]----(1\] and \[\angle PQY + \angle PQR = 180^0--[linear -pair - angles]----(2\]
From (1 and (2 we have
(since RHS of both eq are same)
\[\angle ABX + \angle ABC =\angle PQY + \angle PQR ----(3\]
Now we are given that
\[\angle ABX = \angle PQY -----(4 [given]\]
so from (3 and (4 we have
\[\angle ABC =\angle PQR-------(5\]
Now in △ABC−and−△PQR
we have
AB= PQ (given)
\[\angle ABC =\angle PQR-------from-5\]
BC=QR (given)
Hence \[△ABC \cong △PQR---(by -SAS- test-of -congruency)\]
Thus Proved.

Answer 4

@goformit100 Your problem has been solved. Pls go through it...