The thematic vocabulary in lines, polygons, and triangles for grade 5 math includes:

1. Line: A straight path that extends infinitely in both directions.
2. Line segment: A part of a line with two endpoints.
3. Ray: A part of a line with one endpoint that extends infinitely in one direction.
4. Parallel lines: Lines that never intersect and are always the same distance apart.
5. Perpendicular lines: Lines that intersect at a right angle (90 degrees).
6. Intersecting lines: Lines that cross or meet at a point.
7. Polygon: A closed figure with straight sides made up of line segments.
8. Triangle: A polygon with three sides and three angles.
9. Equilateral triangle: A triangle with all three sides of equal length.
10. Isosceles triangle: A triangle with two sides of equal length.
11. Scalene triangle: A triangle with no sides of equal length.
12. Right triangle: A triangle with one right angle (90 degrees).
13. Acute triangle: A triangle with all three angles less than 90 degrees.
14. Obtuse triangle: A triangle with one angle greater than 90 degrees.
15. Vertex: The point where two sides of a polygon or two rays of an angle meet.
16. Interior angles: The angles inside a polygon or triangle.
17. Exterior angles: The angles outside a polygon or triangle.
18. Congruent: Having the same size and shape.
19. Regular polygon: A polygon with all sides and angles congruent.
20. Quadrilateral: A polygon with four sides and four angles.