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Euclidean Geometry |
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Complex Numbers
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Angle-Side-Angle Method for Triangle
Construction and Duplication.
Given the length of one side and the two adjacent angles, an isometric copy can be constructed. Click on diagram for steps.
Four ASA Variations: If the line segment DF is drawn "horizontally", then the given angles may be drawn above DF with the larger angle at D or the larger angle at F. That gives two isometric triangles. Alternatively, the given angles may be drawn on the down side of DF, again with the larger angle at D or at F. That leads to two more triangles.
ASA Isometry Assumption (and Criteria)
If there is a correspondence between the vertices such that two angles and the included side are isometric then the triangles are isometric. Moreover, both could be built or rebuilt by the same construction ASA method, and each may be moved by a sequence of translations, rotations and/or reflections, so that sides and vertices coincide with the other.An Angle-Side-Angle Method for Triangulization of Position in Navigation
answering the question where were we?
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With the aid of a compass that determines the direction of the north pole, the navigator on a boat or plane at P measures angle PAN and angle PNB in the direction of two points A and B (buoys or landmarks) on land or water, points whose location on the map is known and marked. The navigator then draws rays with those angles from the points A and B. His location at the time of measurement is their P point of intersection. The three points A B and P determine a triangle.
Remark: There is a time delay between measuring the angles and determining the location P on the map. During that time, the boat or plane may have moved away from P. The direction and distance from P may be estimated using the direction and speed of travel away from P.
Remark: Satellite-based GPS (Geo Positioning Systems) give an alternate method for determining the location of P on a paper map or an on-screen display of one.