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# Mathematics 217

### Chapters 11 - 12

Term | Definition |
---|---|

Line | A line has no thickness and it extends forever in two directions. |

Line segment | A subset of a line that contains two points of the line and all points between those two points. |

Ray | A subset of the line AB that contains the endpoint A, the point B, all points between A and B, and all points C on the line such that B is between A and C. |

Skew line | Lines GF and DE are skew lines. They do not intersect, and there is no plane that contains them. |

Concurrent line | Lines DE, EG, and EF are concurrent lines; they intersect at point E. |

Parallel line | Line m is parallel to line n. They have no points in common. |

Axiom | Axioms are statements that cannot be proven and are assumed. |

Theorem | Theorems are statements that can be proven using axioms and logic. |

Half plane | Line AB separates plane "a" into two half-planes. |

Angle | An angle is formed by two rays with the same endpoint. |

Vertex | Vertex is the common endpoint of the two rays that form an angle. |

Sides of an angle | The sides of an angle are the two rays that form an angle. |

Adjacent angle | Adjacent angles are two angles with a common vertex and a common side, but without overlapping interiors. |

Radian | An angle of 1 radian is an angle whose vertex is at the center of a circle and that intercepts an arc equal in length to the radius of the circle. 1 radian ≈ 57.296 degrees |

A line perpendicular to a plane | A line perpendicular to a plane is a line that is perpendicular to every line in the plane through its intersection with the plane. |

Dihedral angle | A dihedral angle is formed by the union of two half-planes and the common line defining the half-planes. |

Dimensional analysis (or unit analysis) | Dimensional analysis (or unit analysis) is a process to convert from one unit of measurement to another. |

Triangle inequality theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. AB + BC > AC |

Perimeter | Perimeter is the length of a simple closed curve, or the sum of the lengths of the sides of a polygon. |

Circle | Circle is the set of all points in a plane that are the same distance from a given point, the center. |

Circumference | Circumference is the perimeter of a circle. |

Pi | Pi is the ratio between the circumference of a circle and the length of its diameter. |

Simple curve | Simple curve is a curve that does not cross itself; starting and stopping points may be the same. |

Closed curve | Closed curve is a curve that starts and stops at the same point. |

Polygon | A polygon is a simple, closed curve with sides that are line segments. |

Convex curve | Convex curve is a simple, closed curve with no indentations; the segment connecting any two points in the interior of the curve is wholly contained in the interior of the curve. |

Concave curve | Concave curve is a simple, closed curve that is not convex; it has an indentation. |

Interior angle | Interior angle is an angle formed by two sides of a polygon with a common vertex. |

Diagonal | Diagonal is a line segment connecting nonconsecutive vertices of a polygon. |

Exterior angle of a convex polygon | Exterior angle of a convex polygon is an angle formed by a side of a polygon and the extension of a contiguous side of the polygon. |

Congruent part | Congruent parts are parts with the same size and shape. |

Regular polygon | If all sides of a polygon are congruent and all angles are congruent, the polygon is a regular polygon. A regular polygon is equilateral and equiangular. |

Right triangle | Right triangle is a triangle containing a right angle. |

Acute triangle | Acute triangle is a triangle in which all the angles are acute. |

Obtuse triangle | Obtuse triangle is a triangle containing an obtuse angle. |

Scale triangle | Scalene triangle is a triangle with no congruent sides. |

Isoceles triangle | Isosceles triangle is a triangle with at least two congruent sides. |

Equilateral triangle | Equilateral triangle is a triangle with three congruent sides. |

Trapezoid | Trapezoid is a quadrilateral with at least one pair of parallel sides. |

Kite | Kite is a quadrilateral with two adjacent sides congruent and the other two sides also congruent. |

Isoceles trapezoid | Isoceles trapezoid is a trapezoid with congruent base angles. |

Parallelogram | Parallelogram is a quadrilateral in which each pair of opposite sides is parallel. |

Rectangle | Rectangle is a parallelogram with a right angle. |

Rhombus | Rhombus is a parallelogram with two adjacent sides congruent. |

Square | Square is a rectangle with two adjacent sides congruent. |

Line of symmetry | Mathematically, a geometric figure has a line of symmetry ℓ if it is its own image under a reflection in ℓ. |

Rotational (turn) symmetry | A figure has rotational symmetry, or turn symmetry, when the traced figure can be rotated less than 360° about some point, the turn center, so that it matches the original figure. |

Point symmetry | Any figure that has rotational symmetry 180° is said to have point symmetry about the turn center. |

Vertical angle | Vertical angles are created by intersecting lines are a pair of angles whose sides are two pairs of opposite rays. |

Supplementary angle | The sum of the measures of two supplementary angles is 180°. |

Complementary angle | The sum of the measures of two complementary angles is 90°. |

Transversal and angle | Angles formed when a line (a transversal) intersects two distinct lines. |

Angle and parallel line property | If any two distinct coplanar lines are cut by a transversal, then a pair of corresponding angles, alternate interior angles, or alternate exterior angles are congruent if, and only if, the lines are parallel. |

The sum of the measures of the interior angles of a triangle | Since the angles appear to form a straight angle, we conjecture that the angles sum up to 180 degrees. |

The sum of the measures of the exterior angles of a convex n - gon | The sum of the measures of the exterior angles of a convex n - gon is 360 degrees. |

Similar object | Similar objects have the same shape but not necessarily the same size. |

Congruent object | Congruent objects have the same shape and the same size. |

Arc | An arc of a circle is any part of the circle that can be drawn without lifting a pencil. |

Center of an arc | The center of an arc is the center of the circle containing the arc. |

Semicircle | If the two arcs determined by a pair of points on the circle are the same size, each is a semicircle. |

Chord | A segment connecting two points on a circle is a chord of the circle. |

Diameter | If a chord contains the center, it is a diameter. |

Triangle congruence | Two figures are congruent if it is possible to fit one figure onto the other so that matching parts coincide. |

Side, side, side congruence condition (SSS) | If the three sides of one triangle are congruent, respectively, to the three sides of a second triangle, then the triangles are congruent. |

Side, angle, side property (SAS) | If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, respectively, then the two triangles are congruent. |

Hypotenuse leg theorem | If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. |

Altitude | An altitude of a triangle is the perpendicular segment from a vertex of the triangle to the line containing the opposite side of the triangle. |

Angle, Side, Angle (ASA) property | If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, respectively, then the triangles are congruent. |

Angle, angle, side (AAS) | If two angles and a side opposite one of these two angles of a triangle are congruent to the two corresponding angles and the corresponding side in another triangle, then the two triangles are congruent. |

Properties of angle bisectors | Any point P on an angle bisector is equidistant from the sides of the angle. same. Any point that is equidistant from the sides of an angle is on the angle bisector of the angle. |

Incenter of a triangle | The angle bisectors of a triangle are concurrent (they intersect in a single point, the incenter) and the three distances from the point of intersection to the sides are equal. |

Similar polygon | Two polygons with the same number of vertices are similar if there is a one-to-one correspondence between the vertices of one and the vertices. |

AA similarity for triangle | If two angles of one triangle are congruent, respectively, to two angles of a second triangle, then the triangles are similar. |

SSS similarity for triangle | If corresponding sides of two triangles are proportional, then the triangles are similar. |

SAS similarity for triangle | Given two triangles, if two sides are proportional and the included angles are congruent, then the triangles are similar. |

Properties of proportion | If a line parallel to one side of a triangle intersects the other sides, then it divides those sides into proportional segments. |

Properties of proportion | If parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on any transversal. |

Midsegment of triangles and quadrilaterals | The midsegment (segment connecting the midpoints of two sides of a triangle) is parallel to the third side of the triangle and half as long. |

Median | A median of a triangle is a segment connecting a vertex of the triangle to the midpoint of the opposite side. |

Center of gravity or centroid | The three medians are concurrent. The point of intersection, G, is the center of gravity, or the centroid, of the triangle. |

Indirect measurement | Similar triangles have long been used to make indirect measurements. |

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marianhood