Changes: Angle of 60°

Revision as of 22:46, 2 December 2020

File:Angle60Detailed.da7c7b029960d7c8bb52725778732097.png

Instruction: Construct an angle of 60° with the given side.

Goal: 3L 3E

Available tools:

Move
Point
Line
Circle
Intersect

Pack: Alpha

Next level: 1.2

3L 3E solution

Let A be the initial point of the given ray.

Construct a circle C1 with center A and an arbitrary radius, intersecting the ray at B
Construct the circle C2 with center B and radius AB, intersecting circle C1 at C and D
Construct line AC

2V solution

Construct line AD

Explanation

All internal angles of an equilateral triangle are 60°, so you just need to construct the two sides of an equilateral triangle adjacent to vertex A. The two circles ensure that AB=AC=BC and AB=AD=BD and so ABC and ABD are equilateral and angles CAB and DAB are 60°.

@@ Line 1: / Line 1: @@
+[[File:Angle60Detailed.da7c7b029960d7c8bb52725778732097.png|center|thumb|400px]]
-{{Delete}}
+<u>Instruction:</u> Construct an angle of 60° with the given side.
+<u>Goal:</u> 3L 3E
+Available tools:
+* Move
+* Point
+* Line
+* Circle
+* Intersect
+<u>Pack:</u> [[Alpha]]
+<u>Next level:</u> [[1.2]]
+==3L 3E solution==
+[[File:1.1-3L 3E.PNG|center|thumb|400px]]
+Let A be the initial point of the given ray.
+# Construct a circle C1 with center A and an arbitrary radius, intersecting the ray at B
+# Construct the circle C2 with center B and radius AB, intersecting circle C1 at C and D
+# Construct line AC
+==2V solution==
+[[File:1.1-2V.PNG|center|thumb|400px]]
+# Construct line AD
+==Explanation==
+All internal angles of an equilateral triangle are 60°, so you just need to construct the two sides of an equilateral triangle adjacent to vertex A.
+The two circles ensure that AB=AC=BC and AB=AD=BD and so ABC and ABD are equilateral and angles CAB and DAB are 60°.
+[[Category:V-stars]]
+[[Category:Level]]