Shaoxing fg slogan

This topic mainly examines the properties of squares, the judgment and properties of congruent triangles, the properties of isosceles right triangle and the comprehensive application of Pythagorean theorem.

In the first question, according to the properties of congruent triangles, it is proved that all triangles ADG are equal to triangle Abbe, and all triangles FAE are equal to triangle GAF.

Solution: (1) Proof: In the square ABCD, because the angle ABE is equal to the angle ADG, AD=AB, in the triangle ABE and triangle ADG, the detailed answer is here. /exercise/math/799732 As shown in the figure, in the square ABCD, points E and F are on the sides BC and CD respectively, and the angle EF=FG=45 degrees.

(2) As shown in the figure, in the isosceles right triangle ABC, the angle BAC=90 degrees, AB=AC, the points M and N are on the side of BC, and the angle MAN=45 degrees. If BM= 1 and CN=3, find the length MN.