Geometry Crossword Puzzle

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Across
  1. 4. a pair of angles that share a common side and a common vertex, but do not overlap.
  2. 7. a straight path that extends indefinitely in both directions.
  3. 10. logical statement that can be derived from another statement by negating both the hypothesis and the conclusion and then reversing their order.
  4. 13. Let ABC be any given triangle. Let O be the circumcenter and K be the symmedian point of triangle ABC. The circle with OK as diameter is the Brocard circle of triangle ABC. The line through O perpendicular to the line BC intersects the Brocard circle at another point A'. The line through O perpendicular to the line CA intersects the Brocard circle at another point B'. The line through O perpendicular to the line AB intersects the Brocard circle at another point C'. (The triangle A'B'C' is the Brocard triangle of triangle ABC.) Let LA be the line through A parallel to the line B'C', LB be the line through B parallel to the line C'A' and LC be the line through C parallel to the line A'B'. Then the three lines LA, LB and LC are concurrent. The point of concurrency is the (point name) of triangle ABC.
  5. 14. a line that intersects two or more other lines at distinct points.
  6. 15. a statement that has been proven to be true through logical reasoning and deduction based on previously established facts or axioms.
  7. 17. the measurement of the size of a surface or a two-dimensional shape.
  8. 18. a line segment from the center of the polygon to the midpoint of one of its sides, forming a right angle with that side.
  9. 21. a pair of adjacent angles formed when two lines intersect.
Down
  1. 1. a type of quadrilateral with all four sides of equal length.
  2. 2. the point where the three angle bisectors of the triangle intersect.
  3. 3. the total distance around the outside of a two-dimensional shape.
  4. 5. the distance around the edge of a closed curve or a circle.
  5. 6. If and only if.
  6. 8. a fundamental element that represents a specific location in space.
  7. 9. a part of a line that is bounded by two distinct endpoints.
  8. 11. the point where the three altitudes of the triangle intersect.
  9. 12. a line segment that connects the midpoints of two sides of a triangle.
  10. 16. the point that divides the segment into two equal parts.
  11. 19. a quadrilateral with at least one pair of parallel sides.
  12. 20. the point where the three medians of the triangle intersect.