Unizor - Geometry2D - Quadrangle - Problems 8
Channel: Zor Shekhtman on UNIZOR Education
Date: 2011-10-30

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1. Construct a trapezoid by a base, two legs and one angle formed by that base with one of its legs.
Note: analyze the number of solutions.
2. Construct a trapezoid by a difference between bases, diagonal and two legs.
3. Construct a trapezoid by its all four sides.
Note: analyze the number of solutions.
4. Construct a trapezoid by its base, altitude onto it and two diagonals.
Note: analyze the number of solutions.
5. Construct a trapezoid by its two bases and two diagonals.
Note: analyze the number of solutions.
6. Construct a parallelogram by two diagonals and an altitude.
7. Construct a parallelogram by a side, sum of two diagonals and an angle between diagonals.
8. Construct a triangle by a side, altitude onto it and a median to another side.
9. Construct a right triangle by a hypotenuse and a sum of two catheti.
10. Construct a right triangle by a hypotenuse and a difference between two catheti.
11. Given a straight line and two points, A and B, not on it, but on the same side from it. Given also a segment MN. Find two points on a line, X and Y, such that a segment XY is congruent to MN and sum of lengths of segments AX + XY + YB is minimal.
Hint: use parallel shift.