Axonometry 2D structures projecting Recent Posts lines, points and angles O octahedron six-trimmed

For some time, I get questions about how to construct a point or segment intersecting two other lines and having some additional properties. It has to do with the problem of four straight, the solution posted on this blog some time ago. So I thought I might want to expand a bit about it and show some simple construction of a similar nature. Here they are. 1 Two points, straight and equal distance
Two points, straight and level sections Draw two circles of the measures at points A and B, and a radius equal to the length of the segment AB. Points of intersection of these circles pointed out that C and D. Lead a simple CD. The intersection of this line with a straight angle mark it as E (big red kropa). Now it's easy to show that AE = BE. 2 Two points, straight and equal angles
Two points, straight and equal angles are simple data k and two points A and B lie on the straight line. From one of these points norwegian epic lead perpendicular to a straight angle. There is a point A. Mark the point of intersection of the straight line perpendicular to k as F. Draw a circle with center F and radius FA. Select the second point of intersection of the circle with the perpendicular. Here is the G-spot. Lead a simple GB and the intersection of this line with a straight mark as C k. It is easy to show that the angles norwegian epic that form a simple AC and BC with a simple k are equal. 3 Two simple point
Given two intersecting straight keel and point M is not lying to them. Run the line through the point M so that the section of the line contained between simple keel was divided into half a point M.
Two point data lines and two intersecting norwegian epic straight keel, and the point M lying between them, and that does not lie on any of these lines. norwegian epic From the point M lead perpendicular to one of the given simple. Here is a simple MB perpendicular to k. Draw a circle with center M and radius MB. Select the second point of intersection of the circle with perpendicular MB as B '. At point B 'lead line parallel to k. The intersection of this line with the line I mark as C. Draw a straight CM and its point of intersection with a simple k mark as D. Arguably, the CM and MD segments have equal length. 4 Two simple, point and equal angles
The data are two lines intersecting at the point A and the point M lying between them. Run the line through the point M so that the angle between the line and each simple data were equal. Solution
Two lines, point and equal angles situation is similar to that of the previous problem. We have a few simple data intersecting at point A and point M does not lie on any of these lines. Draw the complementary angle between simple kili divide it in half straight p. We construct a simple p 'passing through norwegian epic M and parallel to the line p. Simple p 'has the property that it intersects with the straight keel at the same angles.
Structures described here are relatively simple and are suitable norwegian epic for high school geometry class. Many other similar norwegian epic structures can be found in my new book, Essays on geometry and art: the art of geometric constructions.
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Axonometry 2D structures projecting Recent Posts lines, points and angles O octahedron six-trimmed problem with a goat in 3D The sloping cone half cube Archives May 2013 April 2013 March 2013 Categories
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