Geometry: English Vocabulary List

a unit for measuring angles, defined by the angle made when the radius of a circle is laid along its edge

"Measure in radian."

"We measure angles in radian when working with trigonometric functions and circles."

an angle measuring exactly 90 degrees

"The corner made a right angle."

"The corner of a square book forms a right angle that measures exactly ninety degrees."

an angle that measures between 0 and 90 degrees, which is less than a right angle (90 degrees)

"The angle was acute."

"An acute angle measures less than ninety degrees, which makes it smaller than a right angle."

one of a pair of opposite angles made by two intersecting lines, which are always equal

"Vertical angle equal."

"Vertical angles are always equal when two lines intersect each other."

pairs of angles that share a common side and vertex in a polygon or between intersecting lines

"The consecutive angles of a parallelogram are supplementary."

"Consecutive angles between parallel lines and a transversal have special properties."

(geometry) a flat shape consisting of three or more straight sides

"A polygon has sides."

"A polygon is a closed two-dimensional shape formed by straight line segments, such as a triangle or a square."

(geometry) any flat shape with four straight sides, the opposite sides of which are equal and parallel to each other

"A parallelogram is a four-sided shape with opposite sides that are parallel."

"A rectangle is a special type of parallelogram where all four angles are right angles."

a geometric curve formed by the intersection of a plane with two cones, resulting in two symmetrical branches

"The hyperbola has two separate curves."

"A hyperbola is a conic section formed by slicing a double cone at a steep angle"

(geometry) a symmetrical open curve that is similar to the path of an object thrown into the air passes till it falls back to earth

"The parabola is a curve."

"The ball flew in a perfect parabola before landing exactly where the player had aimed it."

(geometry) a flat shape with four equal sides in which opposite angles are equal

"A rhombus has four equal sides."

"A rhombus looks like a slanted square and has four equal sides with equal opposite angles."

a geometric shape with five angles and five straight sides

"A pentagon has five."

"The United States Department of Defense headquarters is famously known as the Pentagon due to its five-sided geometric shape."

(geometry) a polyhedron with four flat sides, a triangular pyramid

"The tetrahedron has four triangular faces."

"A tetrahedron is a three-dimensional shape composed entirely of four triangular faces."

(geometry) a flat shape with four flat sides, two of which are parallel

"The trapezoid has one pair of parallel sides."

"A trapezoid is a quadrilateral with at least one set of parallel sides"

a type of triangle with all three sides of equal length

"Draw equilateral triangle."

"We learned how to draw an equilateral triangle with three equal sides and angles."

a flat geometric shape consisting of three straight sides and one right angle

"Right triangle has."

"A right triangle has one angle that measures exactly ninety degrees."

a triangle in which all three interior angles are less than 90 degrees

"An acute triangle has three small angles."

"All three angles in an acute triangle are less than ninety degrees."

a type of triangle that has two sides of equal length and two angles of equal measure

"An isosceles triangle has two equal sides."

"An isosceles triangle has two sides of equal length and two equal angles opposite those sides."

a type of triangle that has all three sides of different lengths

"A scalene triangle has no equal sides."

"A scalene triangle has three sides of different lengths and three different angles."

a triangle in which one of the interior angles is greater than 90 degrees

"An obtuse triangle has one wide angle."

"An obtuse triangle has one angle that is greater than ninety degrees."

a three-dimensional geometric shape that has a rectangular base and four triangular faces that meet at a single point called the apex

"A rectangular pyramid has a rectangle for a base."

"A rectangular pyramid has a rectangular base and four triangular faces meeting at a point."

a three-dimensional geometric shape with two parallel circular bases connected by a curved surface at a right angle to the bases

"A soda can is a right circular cylinder."

"A right circular cylinder has two circular bases that are parallel and aligned directly above each other."

a solid figure with a circular base and a vertex that is perpendicular to the center of the base

"Right circular cone."

"A right circular cone has a circular base and a curved surface that narrows to a point."

a small circle whose center moves around the circumference of a larger circle

"The old model of the planets used epicycles."

"Ancient astronomers used the epicycle model to explain the motion of planets in the sky."

the longest side of a right-angled triangle, opposite the right angle, and defined as the side opposite the right angle in a right-angled triangle

"The hypotenuse is the longest."

"To find the hypotenuse, you must apply the Pythagorean theorem to any right-angled triangle."

a straight line from one side of a round object, particularly a circle, passing through the center and joining the other side

"The diameter of the circle is ten centimeters."

"The diameter of the tree trunk was so large that two people could not wrap their arms around it."

a point where two or more lines, edges, or rays meet to form an angle, or the point at which the sides of a polygon intersect

"The vertex is here."

"The vertex of the pyramid is the single point at the apex where all the triangular faces meet."

the total length of the external boundary of something

"The guards walked along the perimeter of the army base."

"A perimeter is the continuous boundary line enclosing a defined area"

the total area that the surface of a three-dimensional object occupies

"Calculate surface area."

"We calculate the surface area of the cube to find how much paint we need."

a straight line that a curve approaches indefinitely but never intersects, characterizing the limiting behavior of the curve

"The asymptote is a line the graph approaches."

"An asymptote is a straight line that a curve approaches infinitely closely but never intersects"

a measuring instrument used to measure and draw angles

"Use a protractor to measure the angle."

"Students use a protractor to measure the size of angles accurately in geometry class."

a line that divides a shape into two congruent parts

"Find line of symmetry."

"We find the line of symmetry that divides the shape into two identical halves."

a series of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number

"Study geometric series."

"We study geometric series to understand patterns where each term is multiplied by a constant ratio."

one-fourth of a circle, formed by two perpendicular radii and the connecting arc

"The graph is divided into four quadrants."

"The point lies in the first quadrant of the coordinate plane where both x and y are positive."

an angle formed between two sides of a polygon that lies inside the shape

"Interior angle sum."

"The sum of interior angles in any triangle is always one hundred eighty degrees."

(geometry) a closed plane curve that has two focal points

"An ellipse is oval."

"The orbit of a planet around the sun is not a perfect circle but rather an ellipse with the sun at one focus."

(of a line) intersecting two or more other lines at different points

"Draw a transversal line."

"The transversal line crosses two parallel lines and creates eight angles with special relationships."

to divide something into two equal parts

"The line bisects the angle perfectly."

"The straight line will bisect the circle into two equal halves of exactly the same size and shape."

(geometry) a lack of symmetry or equivalence in shape or size between the two sides or parts of something

"The design's asymmetry made it interesting."

"The architect deliberately introduced asymmetry into the building's design for a unique aesthetic."

the measure of how steep a line is, found by dividing the change in height by the change in horizontal distance

"The slope is steep."

"The gentle slope of the roof ensures efficient water runoff during heavy rainfall."

(geometry) a part of a circle, which is curved

"Draw a long arc."

"The architect designed a graceful arc for the bridge, spanning the river with elegant curvature."

the space between two lines or surfaces that are joined, measured in degrees or radians

"This is a sharp angle."

"The carpenter carefully measured the angle to ensure the two pieces of wood fit together precisely."

(geometry) a flat figure with four straight sides and four angles

"A quadrilateral has four sides."

"A quadrilateral is any polygon with four sides and four vertices including squares rectangles and trapezoids."

the side of a geometric shape, usually the one considered as the bottom, from which the height is measured

"The base is wide."

"The height of the triangle is measured perpendicularly from the base to the opposite vertex."

the length of a straight line drawn from the center of a circle to any point on its outer boundary

"The radius measures five inches."

"The radius of the circular pool was measured from the center to the edge."

(geometry) the length of the external boundary of a curved shape, especially a circle

"Circumference is a length."

"We calculated the circumference of the circular garden to determine how much fencing was needed."

the measurement of a piece of land or a flat surface

"This is a large area."

"The total area of the property, including the garden and patio, is approximately one acre."

the amount of space that a substance or object takes or the amount of space inside an object

"This bottle has a large volume."

"The total volume of the gas increased significantly when the temperature rose."

a straight line that touches a curve or surface at exactly one point, known as the point of tangency

"The tangent touched the circle."

"In calculus, a tangent line provides the instantaneous rate of change for a function at a specific point."

a straight line segment that connects two points on the edge of a circle

"The chord is long."

"This particular chord connects two distinct points on the circumference of the circle, passing through its interior."

(of a straight line) joining opposite corners of a flat shape at an angle

"Draw a diagonal line."

"Draw a diagonal line from the top left corner to the bottom right corner of the square."

(in geometry) describing shapes of the same size and form

"The triangles are congruent."

"The two triangles are congruent because they have the same shape and size."

having an equal distance from each other at every point

"The lines are parallel."

"The two lines are parallel because they run in the same direction and never meet each other."

(of lines or planes) intersecting each other at a 90 degree angle

"The lines are perpendicular."

"The two lines are perpendicular because they intersect at a right angle of ninety degrees."

(geometry) to move a shape or figure from one position to another without rotating, resizing, or otherwise altering its shape

"We can translate the square."

"To translate the triangle, we simply shift its position on the grid without altering its orientation."