Geometry Vocabulary-Cedrique Derouin

ray

One way to think of a ray is a line with one end. A ray starts at a given point and goes off in a certain direction forever, to infinity. The point where the ray starts is called (confusingly) the endpoint. On its way to infinity it may pass through one or more other points.

parallel lines

Parallel Lines. more ... Two lines on a plane that never meet. They are always the same distance apart.

Pythagorean Theorem

Pythagoras Theorem. more ... In a right angled triangle the square of the long side is equal to the sum of the squares of the other two sides. It is stated in this formula: a2 + b2 = c2.

skew lines

Skew Lines. Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions.

right triangle

The right triangle has one 90 degree angle and two acute (< 90 degree) angles. Since the sum of the angles of a triangle is always 180 degrees... y + z = 90 degrees. The two sides of the triangle that are by the right angle are called the legs... and the side opposite of the right angle is called the hypotenuse.

slope rise/run

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

square

The square is probably the best known of the quadrilaterals. It is defined as having all sides equal, and its interior angles all right angles (90°). From this it follows that the opposite sides are also parallel. A square is simply a specific case of a regular polygon, in this case with 4 sides.

triangle sum theorem

The sum of the three angles in any triangle sum to 180 degrees. The importance of this fact in Geometry cannot be emphasized enough. The triangle angle sum theorem is used in almost every missing angle problem, in the exterior angle theorem, and in the polygon angle sum formula.

vertex

Vertex - math word definition - Math Open Reference. Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices.

vertical angles

Vertical Angles are the angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertical angles.

vertical

Vertical is a line that runs straight up and down.

acute angle

acute angle definition. An angle that measures less than ninety degrees but more than zero degrees. (Compare obtuse angle and right angle.)

line symmetry

more ... Another name for reflection symmetry. One half is the reflection of the other half. The "Line of Symmetry" (shown here in white) is the imaginary line where you could fold the image and have both halves match exactly.

obtuse angle

obtuse angle definition. An angle that measures more than 90 degrees but less than 180 degrees. (Compare acute angle and right angle.

rotational symmetry

An object has rotational symmetry if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same. The number of positions in which the object looks exactly the same is called the order of the symmetry.

line of symmetry

Another name for reflection symmetry. One half is the reflection of the other half. The "Line of Symmetry" (shown here in white) is the imaginary line where you could fold the image and have both halves match exactly.

line

A long thin mark made by a pen, pencil, etc. In geometry a line: • is straight (no curves), • has no thickness, and. • extends in both directions without end (infinitely).

point

A point is a dot that marks a spot .

center of rotation

In a rotation, the point that does not move. The rest of the plane rotates around this one fixed point.

diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere.

line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints.

equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

plane

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.

rectangle

It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.

protractor

A protractor is a tool used to measure angles. A protractor is a transparent plastic tool designed to measure angles. They are usually semicircular but also are available in a full circle 360° version.

quadralateral

A quadrilateral is a shape with 4 straight sides.

scalene triangle

A scalene triangle is a triangle that has three unequal sides, such as those illustrated above.

sector

A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. The segment of a circle is the region bounded by a chord and the arc subtended by the chord.

rhombus

A simple (non self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following: a quadrilateral with four sides of equal length (by definition) a quadrilateral in which the diagonals are perpendicular and bisect each other.

ruler

A stick that has numbers in inches and centimeters so that you can measure anything.

reflection

A transformation in which a geometric figure is reflected across a line, creating a mirror image. That line is called the axis of reflection.

rotation

A transformation in which a plane figure turns around a fixed center point. In other words, one point on the plane, the center of rotation, is fixed and everything else on the plane rotates about that point by a given angle.

transformation

A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation. Types of transformations in math. Translation. Reflection.

triangle

A triangle is a shape with 3 angles and 3 sides.

adjacent angles

Adjacent Angles. more ... Two angles are Adjacent when they have a common side and a common vertex (corner point), and don't overlap. See: Adjacent. Adjacent Angles.

obtuse triangle

An acute triangle is a triangle with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180°, no triangle can have more than one obtuse angle.

angle

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

asymmetry

An irregularity or imbalance in the spatial pattern or shape or arrangement of an object or figure is called Asymmetry. For example, when a figure is divided into two unequal halves, it is a case of asymmetry.

isosceles triangle

An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.

trapezoid

A 4-sided flat shape with straight sides that has a pair of opposite sides parallel

paralleogram

A 4-sided flat shape with straight sides where opposite sides are parallel. Also: • opposite sides are equal in length, and. • opposite angles are equal (angles "a" are the same, and angles "b" are the same) NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

central angle

A central angle is the angle that forms when two radii meet at the center of a circle. A central angle is formed at A. Remember that a vertex is the point where two lines meet to form an angle. A central angle's vertex will always be the center point of a circle.

chord

A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the infinite line extension of a chord. More generally, a chord is a line segment joining two points on any curve, for instance an ellipse.

circle

Circle is the locus of points equidistant from a given point, the center of the circle. The common distance from the center of the circle to its points is called radius. Thus a circle is completely defined by its center (O) and radius (R): C(O, R) = O(R) = {x: dist(O, x) = R}.

clockwise

Clockwise is rotating in a circle to the right.

counter clockwise

Counterclockwise is a circle rotating to the left.

polygon

Definition of a Polygon. A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has.

right angle

Definition of a Right Angle. A right angle is an angle that measures exactly 90 degrees. It is exactly a quarter of a circle. When you cut a pie into four equal pieces, the tip of each slice will form a right angle.

transversal

Definition: A line that cuts across two or more (usually parallel) lines. In the figure below, the line AB is a transversal. It cuts across the parallel lines PQ and RS. If it crosses the parallel lines at right angles it is called a perpendicular transversal.

translation

Definition: A translation (notation ) is a transformation of the plane that slides every point of a figure the same distance in the same direction.

acute triangle

Definitions. An acute angle is any angle less than 90 degrees. So, as its name suggests, an acute triangle is a triangle whose three angles are all smaller than 90 degrees.

line of reflection

Each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. In other words, the line of reflection lies directly in the middle between the figure and its image -- it is the perpendicular bisector of the segment joining any point to its image.

congruent

Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent.Feb 21, 2016

horizontal

Horizontal is a line that runs straight from left to right.

straight angle

Straight Angle. more ... A straight angle changes the direction to point the opposite way. It looks like a straight line. It measures 180° (half a revolution, or two right angles)

radius

The Geometry of Circles. Definitions and formulas for the radius of a circle, the diameter of a circle, the circumference (perimeter) of a circle, the area of a circle, the chord of a circle, arc and the arc length of a circle, sector and the area of the sector of a circle.

arc

The arc of a circle is a portion of the circumference of a circle. Measure an arc by two methods: 1) the measure of the central angle or 2) the length of the arc itself.

center of a circle

The center of a circle is the point inside a circle that is the same distance from each point on the circle.

complementary angles

Two Angles are Complementary when they add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees. Examples: 60° and 30° are complementary angles. 5° and 85° are complementary angles.

supplementary angles

Two Angles are Supplementary when they add up to 180 degrees. They don't have to be next to each other, just so long as the total is 180 degrees. Examples: 60° and 120° are supplementary angles.

perpendicular lines

X. Perpendicular means "at right angles". A line meeting another at a right angle, or 90° is said to be perpendicular to it. In the figure above, the line AB is perpendicular to the line DF.