A Euclidean construction. It works by first creating a See the proof below for more on this. This page shows how to construct (draw) a 30 degree angle with compass and straightedge or ruler. See the proof below for more on this. The image below is the final drawing above with the red items added. Using the properties of a rhombus it can be shown that the angle created has a measure of 30 degrees. (third side would be √3 by pythagoras). If you wanted, you could connect P o i n t s D and G and form the equilateral triangle. or when a computer is not available. Inner/outer tangents, regular hexagons and golden section will become a real challenge … It will offer you really complicated tasks only after you’ve learned the fundamentals. Euclidea will guide you through the basics like line and angle bisectors, perpendiculars, etc. $19.99 $ 19. All of them should be constructed simultaneously. The above animation is available as a So, to draw a 30 °, construct a 60 ° angle and then bisect it. In this type of right triangle, the sides corresponding to the angles 30°-60°-90° follow a ratio of 1:√ 3:2. ∆PAS is a right triangle with two sides in the ratio 1:2. A 30 ° angle is half of a 60 ° angle. and then a rhombus Using the properties of a rhombus it can be shown that the angle created has a measure of 30 degrees. diagonal of that rhombus. Hey, D O G, you did it! 99 $20.99 $20.99. In any triangle, smallest angle is opposite shortest side. * A: given (-100.00,0.00)* B: given (100.00,0.00)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (0.00,173.21)line: (AC), * A: given (-100.00,0.00)* B: given (100.00,0.00)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (0.00,-173.21)* D = ⊙AB x ⊙BA (0.00,173.21)line: (CD), * A: given (-100.00,-20.00)* B: given (100.00,20.00)line: (AB)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (34.64,-173.21)* D = ⊙AB x ⊙BA (-34.64,173.21)line: (CD)* E = (AB) x (CD) (0.00,0.00), * A: given (-80.00,80.00)* B: given (80.00,80.00)circle: ⊙ABcircle: ⊙BA* C: given (80.00,-80.00)line: (AC)* E = ⊙AB x ⊙BA (0.00,-58.56)* F = ⊙AB x ⊙BA (0.00,218.56)line: (EF)* G = (AC) x (EF) (0.00,-0.00)* H = (AB) x (EF) (0.00,80.00)circle: ⊙GH, * B: given (81.12,33.99)* C: given (81.12,-33.99)circle: ⊙BC* A: given (-81.12,33.99)circle: ⊙BA* E = (BC) x ⊙BC (81.12,101.96)line: (AE)* F = ⊙BA x (AE) (194.92,149.64)line: (BF)* D: given (-81.12,-33.99)* G = ⊙BC x (AE) (32.67,81.66)line: (DG), * B: given (135.81,63.68)* C: given (142.58,-46.60)circle: ⊙BCcircle: ⊙CB* D = ⊙AB x ⊙BC (55.36,139.41)circle: ⊙DB* E = ⊙CB x ⊙DB (62.13,29.13)line: (BE)* F = ⊙BC x ⊙CB (43.69,2.68)* G = ⊙BC x ⊙CB (234.70,14.40)line: (FG)* H = (BE) x (FG) (0.00,0.00), * B: given (0.00,150.00)* A: given (0.00,0.00)circle: ⊙BA* C = ⊙AB x ⊙BA (129.90,75.00)line: (AC)* D = ⊙AB x ⊙BA (-129.90,75.00)circle: ⊙CD* E = ⊙AB x ⊙CD (0.00,-150.00)* F = (AC) x ⊙CD (354.90,204.90)line: (EF)* G = ⊙AB x (EF) (150.00,0.00)line: (BG)* H = (AC) x ⊙CD (-95.10,-54.90)line: (EH)* I = ⊙AB x (EH) (-150.00,0.00)line: (BI), * A: given (0.00,0.00)* B: given (150.00,0.00)circle: ⊙ABcircle: ⊙BA* D = (AC) x ⊙AB (102.07,109.92)circle: ⊙DA* E = ⊙BA x ⊙DA (252.07,109.92)line: (AE), * A: given (-120.00,-25.40)* B: given (-5.54,123.00)circle: ⊙ABcircle: ⊙BA* D = (AC) x ⊙AB (67.34,-30.72)circle: ⊙DA* E = ⊙BA x ⊙DA (181.80,117.68)line: (AE)* F = (BC) x ⊙BA (145.92,12.62)circle: ⊙FB* G = ⊙AB x ⊙FB (31.46,-135.78)line: (BG)* H = (AE) x (BG) (7.07,34.84), * B: given (0.00,0.00)* A: given (-150.00,0.00)circle: ⊙BA* C = (AB) x ⊙BA (150.00,0.00)circle: ⊙CB* D = ⊙BA x ⊙CB (75.00,129.90)line: (AD), * A: given (-150.00,0.00)* B: given (0.00,0.00)circle: ⊙AB* D = (AC) x ⊙AB (-16.89,69.15)circle: ⊙DB* E = ⊙AB x ⊙DB (-63.75,122.72)line: (AE), * B: given (81.12,33.99)* D: given (-81.12,-33.99)line: (BD)* C: given (81.12,-33.99)* A: given (-81.12,33.99)line: (CA)* E: given (152.10,146.78)* F = (BD) x (CA) (-0.00,0.00)line: (EF), * A: given (-100.00,0.00)* C: given (0.00,79.00)circle: ⊙AC* B: given (-275.10,0.00)circle: ⊙BC* D = ⊙AC x ⊙BC (0.00,-79.00)line: (CD), * C: given (78.00,84.00)* B: given (0.00,0.00)circle: ⊙CB* D = (AB) x ⊙CB (156.00,0.00)line: (CD)* E = ⊙CB x (CD) (0.00,168.00)line: (BE), * C: given (144.61,39.83)* B: given (83.88,124.36)circle: ⊙CB* D = ⊙AB x ⊙CB (135.72,-63.87)circle: ⊙BD* E = ⊙CB x ⊙BD (245.73,15.18)line: (BE), * A: given (112.00,0.00)* C: given (0.00,125.00)circle: ⊙AC* D = (AB) x ⊙AC (-55.84,0.00)circle: ⊙DC* E = ⊙AC x ⊙DC (0.00,-125.00)line: (CE)* F = (AB) x (CE) (0.00,0.00)circle: ⊙CF, * A: given (150.00,0.00)* C: given (-150.00,0.00)line: (AC)* B: given (0.00,-122.20)* D: given (0.00,122.20)line: (BD)* E = (AC) x (BD) (-0.00,0.00)circle: ⊙AE* F = (AB) x ⊙AE (266.29,94.74)* G = (DA) x ⊙AE (33.71,94.74)line: (FG)* H = (BD) x (FG) (0.00,94.74)circle: ⊙EH, * A: given (0.00,0.00)* C: given (0.00,54.11)line: (AC)* B: given (111.00,126.90)circle: ⊙BC* D = (AC) x ⊙BC (-0.00,199.69)line: (BD)* E = ⊙BC x (BD) (222.00,54.11)line: (CE), * A: given (-120.23,10.00)* D: given (87.00,56.00)circle: ⊙AD* B: given (145.00,0.00)circle: ⊙BD* E = ⊙AD x ⊙BD (82.95,-51.47)line: (DE)* C: given (109.70,176.30)circle: ⊙CD* F = ⊙AD x ⊙CD (-11.66,192.41)line: (DF)* G = (AC) x (DE) (91.03,162.79)* H = (AB) x (DF) (127.01,0.68)line: (GH), * D: given (87.00,56.00)* A: given (-100.00,-12.30)circle: ⊙DA* E = (AB) x ⊙DA (279.35,4.67)* F = (AC) x ⊙DA (167.69,238.00)line: (EF), * A: given (-100.00,31.30)* D: given (97.00,65.00)circle: ⊙ADcircle: ⊙DA* E = ⊙AD x ⊙DA (27.69,-122.46)* F = ⊙AD x ⊙DA (-30.69,218.76)line: (EF)* G = (AC) x (EF) (-7.92,85.67)line: (DG)circle: ⊙DG* H = (AB) x ⊙DG (180.48,-1.83)line: (DH), * A: given (0.00,-100.00)* C: given (-66.91,74.31)circle: ⊙ACcircle: ⊙CA* D = (AB) x ⊙CA (-133.83,-100.00)line: (CD)* E = ⊙CA x (CD) (-0.00,248.63)line: (AE)* F = ⊙AC x ⊙CA (117.50,45.11)* G = ⊙AC x ⊙CA (-184.42,-70.79)line: (FG)* H = (AE) x (FG) (-0.00,0.00)circle: ⊙HA, * A: given (-22.40,76.00)* C: given (75.10,-34.40)line: (AC)* B: given (68.40,76.00)* D: given (-99.10,-34.40)line: (BD)* E: given (61.11,196.20)* F = (AC) x (BD) (11.01,38.17)line: (EF), * A: given (0.00,0.00)* B: given (100.00,0.00)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (50.00,-86.60)line: (BC)* D = ⊙BA x (BC) (150.00,86.60)circle: ⊙DA* E = (BC) x ⊙DA (236.60,236.60)line: (AE), * A: given (0.00,0.00)* B: given (165.00,0.00)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (82.50,-142.89)* D = ⊙AB x ⊙BA (82.50,142.89)line: (CD)* E = (AB) x (CD) (82.50,-0.00)circle: ⊙EA* F = (CD) x ⊙EA (82.50,82.50)line: (AF)* G = (CD) x ⊙EA (82.50,-82.50)line: (BG)* H = ⊙AB x (AF) (116.67,116.67)* I = ⊙BA x (BG) (281.67,116.67)line: (HI), * A: given (-201.00,124.00)* B: given (176.00,199.00)circle: ⊙ABcircle: ⊙BA* E = ⊙AB x ⊙BA (52.45,-164.99)* F = ⊙AB x ⊙BA (-77.45,487.99)line: (EF)* C: given (109.00,-76.00)* D: given (-132.00,-120.00)circle: ⊙CDcircle: ⊙DC* G = ⊙CD x ⊙DC (-49.61,110.71)* H = ⊙CD x ⊙DC (26.61,-306.71)line: (GH)* I = (AB) x (EF) (-12.50,161.50)* J = (CD) x (GH) (-11.50,-98.00)line: (IJ)circle: ⊙IJcircle: ⊙JI* K = ⊙IJ x ⊙JI (-236.73,30.88)* L = ⊙IJ x ⊙JI (212.73,32.62)line: (KL)* M = (IJ) x (KL) (-12.00,31.75), * A: given (-100.00,0.00)* B: given (0.00,0.00)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (-50.00,-86.60)* D = ⊙AB x ⊙BA (-50.00,86.60)circle: ⊙CD* E = ⊙BA x ⊙CD (100.00,0.00), * B: given (123.12,0.00)* C: given (0.00,121.24)circle: ⊙BCcircle: ⊙CB* D = (AB) x ⊙BC (295.92,0.00)* E = ⊙BC x ⊙CB (166.56,167.25)line: (DE)* F = ⊙CB x (DE) (86.40,270.89)line: (CF), * A: given (0.00,0.00)* B: given (100.00,0.00)line: (AB)* C = ⊙AB x (AB) (-100.00,0.00)circle: ⊙CA* D = ⊙AB x ⊙CA (-50.00,86.60)* E = (AB) x ⊙CA (-200.00,0.00)line: (DE)* F = ⊙AB x ⊙CA (-50.00,-86.60)line: (FE)line: (AD)* G = (FE) x (AD) (100.00,-173.21)line: (BG), * C: given (79.62,60.50)* B: given (100.00,0.00)circle: ⊙CB* D = ⊙AB x ⊙CB (26.79,96.34)circle: ⊙BD* E = ⊙CB x ⊙BD (100.00,121.00)circle: ⊙EB* F = ⊙BD x ⊙EB (204.79,60.50)line: (BF)* G = ⊙BD x ⊙EB (-4.79,60.50)line: (BG)* H = ⊙AB x (BF) (-50.00,-86.60)* I = ⊙AB x (BG) (-50.00,86.60)line: (HI), * A: given (119.88,-11.01)* C: given (282.12,-78.99)line: (AC)* B: given (282.12,-11.01)* D: given (119.88,-78.99)line: (BD)* E: given (-189.77,-68.90)* G: given (-260.23,-243.10)line: (EG)* F: given (-137.90,-120.77)* H: given (-312.10,-191.23)line: (FH)* I = (AC) x (BD) (201.00,-45.00)* J = (EG) x (FH) (-225.00,-156.00)line: (IJ), * A: given (-80.00,0.00)* B: given (0.00,0.00)circle: ⊙ABcircle: ⊙BA* C = (AB) x ⊙BA (80.00,0.00)circle: ⊙CA* D = (AB) x ⊙AB (-160.00,0.00)circle: ⊙DB* E = ⊙CA x ⊙DB (-40.00,105.83)circle: ⊙AE* F = (AB) x ⊙AE (33.14,0.00), * B: given (0.00,0.00)* A: given (-80.00,0.00)circle: ⊙BA* C = (AB) x ⊙BA (80.00,0.00)circle: ⊙CB* D = ⊙BA x ⊙CB (40.00,-69.28)circle: ⊙AD* E = (AB) x ⊙AD (58.56,0.00), * A: given (0.00,0.00)* B: given (100.00,0.00)circle: ⊙ABcircle: ⊙BA* C = (AB) x ⊙AB (-100.00,0.00)circle: ⊙CA* D = ⊙AB x ⊙CA (-50.00,-86.60)line: (BD)* E = ⊙BA x (BD) (186.60,50.00)line: (AE), * A: given (-75.00,0.00)* B: given (75.00,0.00)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (0.00,-129.90)line: (AC)* D = ⊙AB x (AC) (-150.00,129.90)line: (BD)* E = ⊙BA x (BD) (-54.90,75.00)circle: ⊙EB* F = ⊙BA x ⊙EB (75.00,150.00)line: (BF)* G = ⊙AB x ⊙EB (-204.90,75.00)line: (EG)* H = ⊙BA x (BD) (204.90,-75.00)* I = ⊙BA x ⊙EB (-54.90,-75.00)line: (HI)circle: ⊙EA* J = ⊙AB x ⊙EA (-75.00,150.00)line: (AJ), * A: given (0.00,75.00)* B: given (75.00,0.00)line: (AB)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (-27.45,-27.45)* D = ⊙AB x ⊙BA (102.45,102.45)line: (CD)* E = (AB) x (CD) (37.50,37.50)circle: ⊙EA* F = (CD) x ⊙EA (75.00,75.00)line: (AF)line: (BF)circle: ⊙AF* G = (AB) x ⊙AB (-75.00,150.00)* H = (AF) x ⊙AF (-75.00,75.00)line: (GH)* I = (AB) x ⊙BA (150.00,-75.00)* J = (CD) x (GH) (-75.00,-75.00)line: (IJ), * A: given (-100.00,0.00)* C: given (0.00,79.00)line: (AC)circle: ⊙AC* D = (AB) x ⊙AC (-227.44,0.00)* E = (AC) x ⊙AC (-200.00,-79.00)circle: ⊙DE* F = ⊙AC x ⊙DE (-200.00,79.00)line: (CF), * A: given (-100.00,0.00)* B: given (100.00,0.00)circle: ⊙AB* C: given (-80.00,80.00)circle: ⊙AC* D = (AC) x ⊙AC (-120.00,-80.00)circle: ⊙BD* E = (AB) x ⊙AB (-300.00,0.00)circle: ⊙CE* F = ⊙AB x ⊙CE (76.47,-94.12)line: (BF)* G = ⊙AC x ⊙BD (-120.00,80.00)line: (CG), * A: given (-100.00,0.00)* B: given (0.00,79.00)line: (AB)circle: ⊙AB* C: given (-275.10,0.00)* D = (AB) x ⊙AB (-200.00,-79.00)circle: ⊙CD* E = ⊙AB x ⊙CD (-200.00,79.00)line: (BE), * A: given (-100.00,-35.00)* B: given (87.30,35.00)line: (AB)circle: ⊙ABcircle: ⊙BA* C = ⊙AB x ⊙BA (54.27,-162.21)* D = ⊙AB x ⊙BA (-66.97,162.21)line: (CD)* E: given (235.00,0.00)* F = (AB) x (CD) (-6.35,0.00)line: (EF).

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