2022 Examination Finale: Chord Diagram and Vertical Model (2)

【Analysis】 (1) Ce∥AB know ∠E=∠EBA, ∠ECA=∠A, by the nature of the isosceles triangle know AB = CB, combined with CE = CD know AB = CE, thus obtaining evidence. (2) Find the G point on EF so that FG = CF, easy to prove △ CFG is an equilateral triangle, you can get CG = CF = GF, you can get ∠ECG = ∠ ACD, you can prove △ ECG ≌ △ CDF, you can get DF = EG, you can solve the problem; (3) find the H point on the FP, so that FH = FG, easy to prove △ FGH is an equilateral triangle, you can get ∠ GHF = ∠ FGH = 60 °, GH = FG = FH, you can find ∠ FGD = ∠ QGH, It can be proved that △DFG ≌ △ QHG can be obtained, and DF = QH can be obtained, and the problem can be solved.

【Analysis】【Scenario observation】Mr= RN, ∠MRN = 90° are obtained according to the properties of isosceles right triangles, ∠PMR=∠NRQ is obtained according to the properties of the cogeneration angle, and conclusions are obtained according to the properties of the full isometric triangle;

【Problem Exploration】 According to the quadrilateral ACEF is a square, AC = CE is obtained, ∠ACE = 90 ° is obtained according to the nature of the cogeneration ∠ BAC = ∠ ECK, EK = BC can be obtained according to the nature of the full equal triangle, the same reason is obtained BC = HI, and the conclusion can be obtained by equal substitution;

【Extended Extension】According to the quadrilateral ACEF is rectangular, ∠ACE=90°, according to the nature of the cohesive angle to get ∠BAC=∠ECM according to the properties of similar triangles to get BC=kEM, the same theory to get BC=kHN, the equivalent substitution to get EM=HN, the introduction of △NHT≌△EMT, according to the properties of the full equal triangle can be concluded.