Geometry Notes
1.
Geometry –
a branch of mathematics which studies the
relationship of points, lines, angles, surface,
and figures in space, including the definition,
comparison and measurement of plane and solid
figures.
2.
Point -
an exact location in space, usually represented
by a dot.
.
A
3.
Line -
AB
4.
Line Segment -
AB
a straight path in a plane, extending in both
directions with no endpoint.
.
.
A
B
a part of a line between two endpoints
A
B
5.
Ray -
a part of a line; it begins at one endpoint, and
extends forever in one direction.
AB
6.
Angle -
‹B
‹ABC
‹CBA
7.
Vertex -
A
B
a figure formed by two rays that meet at a
common endpoint
A
B
C
the point where 2 or more rays meet; the
point of intersection of two sides of a polygon;
the point of intersection of 3 or more edges
of a solid figure; the top point of a cone.
Vertex
8.
Protractor -
a tool used for measuring or drawing angles.
9.
Degree -
a unit for measuring angles or for measuring
temperature
10. Congruent -
having the same size and shape
11. Plane -
a flat surface that extends without end in all
directions
12. Polygon -
a closed plane figure formed by 3 or more
straight sides that are line segments.
Kinds of Angles
13. acute angle -
an angle whose measure is greater than 0˚ and
less than 90˚
14. obtuse angle - an angle whose measure is greater than 90˚
and less than 180˚
15. right angle -
an angle which is half of a straight angle;
its measure is exactly 90˚
16. straight angle - an angle whose measure is 180˚
17. supplementary angles – 2 angles whose measures have a sum
of 180˚; they form a straight angle.
80˚
100˚
18. complementary angles – 2 angles whose measures have a sum
of 90˚; they form a right angle.
45˚
45˚
19. vertical angles – a pair of opposite congruent angles formed
where 2 lines intersect.
Ex. 2 and 4 are vertical angles; 1 and 3 are vertical angles
2
1
3
4
20. adjacent angles – side-by-side pairs of angles that have a
common vertex and a common ray.
Ex. 2 and 3 are adjacent angles. Can you name other pairs?
2
1
3
4
Kinds of Lines
21. intersecting lines – lines that cross each other at exactly one
point
22. parallel lines – lines in a plane that are always the same
distance apart. Parallel lines never
intersect.
23. perpendicular lines – intersect to form 90˚, or a right angle.
Kinds of Planes
24. parallel planes – always the same distance apart. If parallel
planes were extended without end, they would
never intersect.
25. intersecting planes – planes that cross each other are called
intersecting planes. They intersect at a
line.
26. perpendicular planes – planes that intersect at right angles.
Kinds of Polygons
Polygons are classified by the number of their sides, angles and
vertices. A regular polygon is a polygon in which all sides are
congruent and all angles are congruent.
27. triangle -
a polygon with 3 sides, 3 angles and 3 vertices
28. quadrilateral - a polygon with 4 sides, 4 angles and 4 vertices
29. pentagon -
a polygon with 5 sides, 5 angles and 5 vertices
30. hexagon -
a polygon with 6 sides, 6 angles and 6 vertices
31. septagon / heptagon - a polygon with 7 sides, 7 angles and 7
vertices
32. octagon -
a polygon with 8 sides, 8 angles and 8 vertices
33. nonagon -
a polygon with 9 sides, 9 angles and 9 vertices
34. decagon - a polygon with 10 sides, 10 angles and 10 vertices
Kinds of Quadrilaterals
35. parallelogram -
a quadrilateral whose opposite sides are
parallel and congruent (same length)
36. rectangle -
a parallelogram with 4 right angles
37. square -
a rectangle with 4 congruent sides
38. rhombus -
parallelogram with 4 congruent sides
(a “tilted square”)
39. trapezoid - a quadrilateral with exactly 1 pair of parallel
sides
Kinds of Triangles
40. scalene triangle - a triangle with NO congruent sides
41. equilateral triangle - a triangle with three congruent sides
42. isosceles triangle - a triangle with exactly two congruent sides
43. right triangle - a triangle with one right angle
44. acute triangle - a triangle with ALL angles less than 90°
45. obtuse triangle - a triangle with ONE angle greater than 90°
46. regular polygon - a polygon in which all sides are congruent
and all angles are congruent.
47. line of symmetry - a line across which a figure is symmetric
48. similar polygons - figures with the same shape, but not
necessarily the same size
49. congruent polygons - figures having the same shape AND are
the same size
50. circle -
the set of all points a given distance from a point
called the center
51. arc - a curved line drawn between two points along the
circumference of a circle
52. chord - a line segment with endpoints on a circle
53. diameter - a line segment that passes through the center of
a circle and has its endpoints on the circle
54. radius -
a line segment with one endpoint at the center of
the circle and the other endpoint on the circle
55. circumference - the distance around a circle