As shown in the figure, in the quadrilateral ABCD, ab = CD, BF = De, AE ⊥ BD, CF ⊥ BD, e and f respectively. (1) prove: △ Abe ≌ △ CDF; (2) if AC and BD intersect at point O, prove: Ao = Co

As shown in the figure, in the quadrilateral ABCD, ab = CD, BF = De, AE ⊥ BD, CF ⊥ BD, e and f respectively. (1) prove: △ Abe ≌ △ CDF; (2) if AC and BD intersect at point O, prove: Ao = Co

It is proved that: (1) be = DF, ∵ AE ⊥ BD, CF ⊥ BD, ∵ AEB = ∠ CFD = 90 degree, ∵ AB = CD, ∵ RT △ Abe ≌ RT △ CDF (HL); (2) connect AC, intersect BD at O, ? Abe ≌ CDF, ? Abe = ∠ CDF, ≌ ab ∥ CD, ? AB = CD, ≌ quadrilateral ABCD is parallelogram, ≌ Ao = Co

As shown in the figure, in ladder ABCD, ab ‖ DC and E are the midpoint of BC, and the extension lines of AE and DC intersect at point F to connect AC and BF. What quadrilateral is abfc? Please give reasons

The reason is as follows: ∵ be = CE, ab ∥ DC ≌ FEC ≌ AEB (AAS) ≌ AE = EF ∵ ab ∥ CF ∥ quadrilateral abfc is a parallelogram

As shown in the figure, in ladder ABCD, ab ‖ DC and E are the midpoint of BC, and the extension lines of AE and DC intersect at point F to connect AC and BF. What quadrilateral is abfc? Please give reasons

The reason is as follows: ∵ be = CE, ab ∥ DC ≌ FEC ≌ AEB (AAS) ≌ AE = EF ∵ ab ∥ CF ∥ quadrilateral abfc is a parallelogram

As shown in the figure, it is known that e is a point on the edge CD of rectangular ABCD, BF ⊥ AE is in F, try to explain: △ Abf ∽ EAD

It is proved that: in ∵ rectangular ABCD, ab ∥ CD, (2 points) ∥ BAF = ∠ AED. (4 points) ∥ BF ⊥ AE, ∥ AFB = 90 °, ∥ AFB = ∠ d = 90 ° (5 points) ∥ Abf ∥ EAD. (6 points)