The seventh grade mathematical geometry proof questions, there are (written in brackets known, equivalent replacement or something)

∠∠BAP and ∠APD are complementary (known).

∴AB is parallel to CD (complementary to the lateral inner angle, two straight lines are parallel)

∴∠BAP=∠APC(？ Two straight lines are parallel and have equal internal dislocation angles)

∫≈ 1 =∠2 (known)

∴∠BAP-∠ 1=∠APC-∠2

That is, ∠EAP=∠PFE (the nature of the equation)

∴AE is parallel to FP (internal dislocation angles are equal and two straight lines are parallel)

∴∠e =∞∞∠f (two straight lines are parallel and the internal dislocation angles are equal)

Proof: ∫BD//CE is known

∴∠C+∠DBC= 180？ These two lines are parallel and complementary.

∠∠C =∠D known.

∴∠D+∠DBC= 180 equivalent substitution

∴DF//AC？ The internal angles on the same side are complementary and the two straight lines are parallel.

∴∠？

3. As shown in the figure

∫AB∨CD，

∴∠ 1=∠D，

∵∠ 1+∠ Abe +∠ CDE = 360 (the sum of the internal angles of the triangle is 360).

∴∠B+∠E+∠D=360

4.( 1) (not necessarily)

(2) Parallel

∫∠BAD =∠BCD，AD∨BC，

That is af∨EC.

∴ ∠BCF=∠CFD (two straight lines are parallel and the internal dislocation angles are equal).

∫AE and CF divide∠ ∠BAD and∠ ∠BCD equally, respectively.

∴ ∠FAE=∠BCF。

∴ ∠FAE =∠CFD。

∴cf∑AE (same angle, two straight lines are parallel).

(3) It is parallel