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Definitions for Geometry

email Scott Turner

These definitions are an essential part of a high school geometry course, which I taught to my two sons four years apart. You can't do math without knowing your terms. Some of these definitions differ from those in standard books, but they describe the same concepts.

right angle
A half-circle divided into 2 equal angles forms 2 right angles. A right angle is an angle whose size matches one of these.
acute angle
An acute angle is any angle smaller than a right angle.
obtuse angle
An obtuse angle is any angle bigger than a right angle and not a stright angle.
straight angle
A straight angle an angle whose 2 rays, when combined, form a line.
If 2 particular lines are the same distance from one another all along the lines, then they are parallel. Any other lines are not parallel.
Two lines are parallel if and only if all along the lines they are the same distance from one another.
Perpendicular is 2 lines crossing such that there are 4 right angles formed.
complementary angles
Any 2 angles that, if connected, would form a right angle, are complementary.
supplementary angles
Any 2 angles that, if connected, would form a straight angle, are supplementary.
vertical angles
Vertical angles are formed by 2 intersecting lines. They are on opposite sides and they are perfectly equal.
linear pair of angles
A linear pair is connected and makes 180 degrees in a plane.
diagonal (of a polygon)
A diagonal of a polygon is a line segment which goes from one corner of the polygon to another, through the interior of the polygon.
equilateral polygon
An equilateral polygon is any polygon whose sides are all equal in length.
equiangular polygon
An equiangular polygon is any polygon with all its angles the same size.
regular polygon
A regular polygon is a polygon which is both equiangular and equilateral.
right triangle
A right triangle is any triangle that hsa a right angle.
acute triangle
An acute triangle is any triangle whose angles are all smaller than a right angle.
obtuse triangle
An obtuse triangle is any tringle with one of its angles larger than a right angle.
scalene triangle
A scalene triangle is any triangle which does not have any sides equal to one another.
isosceles triangle
An isosceles triangle is any triangle which has 2 or more sides that are equal in length.
median of a triangle
A median of a triangle is a line segment starting at one vertex of a triangle and ending at the other side, where it splits the side in 2 equal halves.
altitude of a triangle
An altitude of a triangle is a line segment from a vertex and ending at a point on the line through the other 2 vertices, which is perpendicular to that line.
A trapezoid is a quadirilateral with exactly 2 sides parallel.
A kite is a quadrilateral that has 2 pairs of adjacent equal sides, but all 4 are not equal to each other.
A parallelogram is a quadrilateral with 2 pairs of parallel sides.
A rhombus is an equilateral quadrilateral.
A rectangle is a quadrilateral with all of its angles of equal measure.
A square is an equiangular, equilateral quadrilateral.
midsegment of a triangle
The segment connecting the midpoints of two sides of a triangle is called the midsegment of a triangle.
midsegment of a trapezoid
The line segment connecting the midpoints of the two nonparallel sides of a trapezoid is called the midsegment of the trapezoid.
A vector is a quantity that has both direction and magnitude.
vector sum
The vector sum, or resultant vector of two or more vectors is the single vector that has the same effect.
A circle is the set of all points in a plane at a given distance from a given point in the plane.
arc of a circle
An arc of a circle consists of two points on the circle and the continuous (unbroken) part of the circle between the two points.
A semicircle is an arc of a circle whose endpoints are the endpoints of a diamenter.
minor arc
A minor arc is an arc of a circle that is less than a semicircle of the circle.
major arc
A major arc is an arc of a circle that is greater than a semicircle of the circle.
tangent circles
Tangent circles are two circles that are tangent to the same line at the same point.
A quadrilateral inscribed in a circle is called a cyclic quadrilateral.

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