大学选修课论文有这个的参考下吧

2. A known point for a straight line parallel to the known straight line.

Set A is known point, BC is known straight line, after A request to do A straight line parallel to BC Take A little D took office in BC, connection AD in straight DA points on A, do < DAE = < ADC A straight line is straight line EA AF

∴ linear AD and two straight lines BC, EF into each other NaCuoJiao intersection equal EAD, ADC

∴ EAF ∥ BC

3. In line for a known on the square.

Line AB is a known, in the line AB requirements on a square

The line AB to AC from point A are painting of the straight line, it and AB, at right angles Take AD = AB

大学选修课论文有这个的参考下吧

Lead point D do DE, parallel to the AB, lead point B do BE parallel to the AD, so ADEB is a parallelogram ∴ AB = DE, AD = BE

And AD = AB

∴ parallelogram ADEB is equal sides ∵ < BAD + < ADE = 180 ° < BAD is right angles ∴ < ADE is right angles

∴ parallelogram edge and diagonal in equal ∴ ABDE is a square

4: known line by a known to do a straight line and linear known at right angles

Solution: take a little arbitrary in AC D, make CE = CD In DE make one FDE equilateral triangle Connection FC ∵ DC CE CF = CF DF = CF

大学选修课论文有这个的参考下吧

DF = FE

∴ < DCF = < ECF

They are LinJiao, by definition 10, both is right angles

Proposition proof:

Proposition 1: if two triangle has both sides were equal to both sides, and the equal line

between equal the Angle. So, they are equal to the lower side of the bottom edge, triangle is equal to the triangle, and other Angle is equal to other Angle, namely that the Angle to the sides. Proof: set ABC, DEF is two triangles, AB = DE, AC = DF, < BAC = < EDF If mobile triangle ABC to DEF, if A fall in point D, and line in the paragraph DE ∵ AB = DE

∴ B and E coincidence And AB and DE superposition < BAC = < EDF

∴ AC and DF superposition

And AC = DF

大学选修课论文有这个的参考下吧

∴ C and F coincidence

∴ enables delta ABC and train DEF coincidence, that is congruent

Proposition 2: a straight line and the other a straight line pay into horn, or two right angles,

or is their and equal to two right angles

Proof: set any straight line AB/CD into Angle CBA, ABD If < CBA = < ABD

The < CBA = < ABD = 90 ° (definition 10) If both not right angles BE as an CD in B < CBE = < EBD = 90 ° < CBE = < CBA + < ABE

∴ < CBE + EBD < = < CBA + < ABE + < EBD Similarly, < DBA + < ABC = < DBE + < EBA + < ABC ∴ < CBE + EBD < = < DBA + < ABC = 180 ° Original proposition find