Unizor - Geometry2D - Triangles - Construction 4
Channel: Zor Shekhtman on UNIZOR Education
Date: 2011-10-14

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This lecture is about how to construct some simple geometrical objects and perform basic construction operations.
The following problems are addressed:
1. Given a straight line and two points anywhere on a plane. Construct a point on a given line equidistant to two given points.
2. Construct a point equidistant to three vertices of a given triangle.
3. Given an angle and a straight line that crosses both its sides. Construct a point on this line equidistant to two sides of a given angle.
4. Construct a point equidistant to three sides of a given triangle.
5. Given a straight line PQ and two points M and N outside it, but on the same side from it. Construct a point X on the line PQ such that angles ∠PXM and ∠QXN are congruent.
6. Construct a right triangle by one of its catheti and a sum of hypotenuse and the other cathetus.
7. Construct a triangle by a side, an angle it makes with another side and a sum of two other sides.
8. Given an angle and two points, one on each side of an angle. Construct a point equidistant from both sides of an angle and, at the same time, equidistant from two given points on angle's sides.
Notice, that distances to angle's sides should be equal to each other, but not necessarily equal to distances to given points.