Tuesday, May 21, 2024

1.5. Isosceles triangles and symmetry, Kiselev's Geometry, Book I. Planimetry, Givental Alexander.


 Exercises.

63.* How many axes of symmetry can a quadrilateral have?

Solution: A quadrilateral can have at most four axes of symmetry.

66.* Two points A and B are given on the same side of a line MN. Find a point C on MN such that the line MN would make congruent angles with the sides of the broken line ACB.

Solution: 

The figure above gives the solution to the problem.

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1.8. Right triangles, Kiselev's Geometry, Book I. Planimetry, Givental Alexander.

  Exercises. Prove Theorems: 103.* A line and a circle can have at most two points in common. Proof: Assume that a line and a circle have th...