As shown in the figure, it is known that p is a point outside the square ABCD. Pa = 1，Pb = 2。 Rotate △ ABP 90 clockwise around point B, so that point P rotates to point P ′, AP ′ = 3, and find the degree of ∠ BP ′ C. 。

answer

Solution: connect PP',

∫△ABP rotates 90 clockwise around point B to rotate point P to point P',

∴p′b=pb=2,∠pbp′=90，

∴pp′=

PB2+P′B2 = 2

2，∠BPP′= 45，

∫PA = 1，AP′= 3，

∴pa2+pp′2=ap′2，

∴∠app′=90，

∴∠apb=∠app′+∠bpp′= 135，

∴∠bp′c=∠apb= 135。

analyse

First connect PP', and we can get the length of PP' and ∠ BPP' = 45 from the nature of rotation, and then we can prove that ∠ APP' = 90 from the inverse theorem of Pythagorean theorem, and then get the answer.

This topic examines the nature of rotation, the nature of isosceles right triangle and the inverse theorem of Pythagorean theorem. This question is moderately difficult. Pay attention to mastering the method of auxiliary lines, the corresponding relationship between graphics before and after rotation, and the application of the idea of combining numbers with shapes.