Confusion over SSA axiom for congruency

Question

I was browsing through KHAN Academy videos when I met the one which Explained why SSA is not a Congruency postutate. But I had this Diagram in my Mind(Different from the video)

Click Here to see diagram

Sorry that I cannot embed the image, as I have insufficient reputation

Here

AC = PR, BC = QR, ANGLE A = ANGLE P

Now I feel that this information is enough to prove the Triangles congruent but my Book has no mention of it. Please Explain

Answer 1

No, it is not.

See SSA

"Side-Side-Angle condition: If two sides and a corresponding non-included angle of a triangle have the same length and measure, respectively, as those in another triangle, then this is not sufficient to prove congruence; but if the angle given is opposite to the longer side of the two sides, then the triangles are congruent. The Side-Side-Angle condition does not by itself guarantee that the triangles are congruent because one triangle could be obtuse-angled and the other acute-angled."

Regarding your drawing, you may consider a circle centered in $C$ with radius $CB$ : it will intersect the side $AB$ into $B_1$ with $CB=CB_1$.