Example 1:
It is known that AB=CD, ∠A=∠D, and verification ∠ B = ∠ C.
2. Line segment continuation method: After line segment extension, the extended line segment meets certain conditions, and a new congruent triangles solution is constructed.
Example 2: in △ABC, ∠ BAC = 90, ∠ AB=AC, ∠ ABC = ∠ ACB = 45, D is the midpoint of AC, AE⊥BD is in F, BD is in E. Verify ∠ ADB = ∠ CDD.
3. Equilateral method: When encountering the bisector of an angle, make both sides of the angle equal and construct a new congruent triangles to solve the problem.
Example 3: AD is the bisector of △ABC, AB > AC BAC in AC, and P is the point on AD. Verify AB-AC > BP-PC.
4. Distance equality method: Take the points on the bisector of the angle to make the distances on both sides of the angle equal, and construct a new congruent triangles problem solving.
Example 4: In △ABC, AD is the bisector of △ ∠BAC, and BD=DC. Prove AB=AC.
5. Interception Complementarity: When proving the sum, difference or multiplication relation of line segments, intercept or extend short line segments on long line segments to construct a new congruent triangles to solve the problem.
Example 5: E is a point on the CD beside the square ABCD, and F is on BC, ∠DAE=∠FAE, and verification AF = AD+CF.