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ACT Math and Assessment - Geometry

Here you will learn some English words related to geometry, such as "tangent", "vertex", "ellipse", etc. that will help you ace your ACTs.

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ACT Vocabulary for Math and Assessment
slope
slope
[noun]

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

Ex: The slope of the line between points (1, 2) and (3, 6) is 2. 
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arc
arc
[noun]

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

Ex: In a circle, a minor arc is shorter than a major arc. 
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radian
radian
[noun]

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

Ex: An angle of 1 radian means the arc length is the same as the radius of the circle. 
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radius
radius
[noun]

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

Ex: The radius of a circle is half the length of its diameter, extending from the center to any point on the circumference. 
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diameter
diameter
[noun]

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

Ex: The diameter of a circle is the longest distance between any two points on its circumference, passing through the center. 
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perimeter
perimeter
[noun]

the total length of the external boundary of something

Ex: The geometry student calculated the perimeter of the rectangular garden to determine how much fencing would be needed. 
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circumference

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

Ex: The formula for finding the circumference of a sphere involves multiplying the diameter by π (pi). 
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area
area
[noun]

the measurement of a piece of land or a flat surface

Ex: The area of a rectangle can be calculated by multiplying its length by its width. 
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volume
volume
[noun]

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

Ex: The volume of water in the glass was 250 milliliters. 
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angle
angle
[noun]

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

Ex: She used a protractor to measure the angle of the triangle accurately. 
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right angle

an angle measuring exactly 90 degrees

Ex: To construct a square, each corner must form a perfect right angle. 
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vertical angle

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

Ex: Vertical angles are always congruent to each other. 
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interior angle

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

Ex: Each interior angle of a regular pentagon measures 108 degrees. 
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acute angle

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

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consecutive angle

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

Ex: In a parallelogram, consecutive angles are supplementary, meaning their measures add up to 180 degrees. 
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obtuse
obtuse
[Adjective]

(of angle) greater than 90 degrees but less than 180 degrees

Ex: The angle formed by the hands of the clock at 2:30 is obtuse, measuring approximately 120 degrees. 
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protractor

a measuring instrument used to measure and draw angles

Ex: The teacher used a protractor to show how to measure angles in the geometry lesson. 
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perpendicular
perpendicular
[Adjective]

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

Ex: In technical drawings, architects ensure walls are precisely perpendicular to allow for square structures. 
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polygon
polygon
[noun]

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

Ex: A triangle is the simplest type of polygon with three sides. 
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parallelogram

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

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tetrahedral
tetrahedral
[Adjective]

characterized by or resembling a tetrahedron, which has four triangular faces

Ex: The chemist explained that a methane molecule has a tetrahedral geometry, with the carbon atom at the center. 
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trapezoid
trapezoid
[noun]

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

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pentagon
pentagon
[noun]

a geometric shape with five angles and five straight sides

Ex: The flag of the city had a pentagon in the center, symbolizing the five founders. 
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quadrilateral

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

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rhombus
rhombus
[noun]

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

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epicycle
epicycle
[noun]

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

Ex: The concept of an epicycle allows for the modeling of complex periodic movements in geometry and astronomy. 
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hyperbola
hyperbola
[noun]

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

Ex: The hyperbola is a conic section formed by intersecting a plane with two cones on opposite sides of the plane. 
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parabola
parabola
[noun]

(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

Ex: The path of a thrown ball forms a parabola. 
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ellipse
ellipse
[noun]

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

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right triangle

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

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acute triangle

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

Ex: In an acute triangle, each angle measures less than 90 degrees. 
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equilateral triangle

a type of triangle with all three sides of equal length

Ex: Each side of an equilateral triangle is the same length. 
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scalene triangle

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

Ex: The sides of a scalene triangle are not equal in length. 
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isosceles
isosceles
[Adjective]

describing a triangle with at least two sides of equal length

Ex: The triangle has two equal sides, making it an isosceles triangle. 
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hypotenuse

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

Ex: In a right-angled triangle with legs of length 3 and 4 units, the hypotenuse can be calculated using the Pythagorean theorem as √(3² + 4²) = 5. 
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right circular cylinder

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

Ex: To find the surface area of a right circular cylinder, you need to account for both the lateral surface area and the area of the two bases. 
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rectangular pyramid

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

Ex: In the art project, students created models of rectangular pyramids using cardboard for the base and sides. 
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asymmetry
asymmetry
[noun]

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

Ex: In geometry, asymmetry means the two sides are not identical. 
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vertex
vertex
[noun]

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

Ex: In a triangle, each of its three corners is a vertex where two sides meet. 
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diagonal
diagonal
[noun]

a straight line connecting opposite corners of a flat shape at an angle

Ex: The rectangle's diagonal was longer than its sides. 
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congruent
congruent
[Adjective]

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

Ex: If you fold the paper along the crease, the two halves are congruent. 
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base
base
[noun]

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

Ex: In a triangle, the base is the side used to calculate the height for finding the area. 
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parallel
parallel
[noun]

a pair of geometric figures, such as lines or planes, that do not meet or intersect, no matter how far they are extended

Ex: The two parallels in the diagram never intersect. 
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line of symmetry

a line that divides a shape into two congruent parts

Ex: A circle has an infinite number of lines of symmetry because it can be divided into two equal halves along any diameter. 
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geometric series

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

Ex: The geometric series 2, 4, 8, 16, ... has a common ratio of 2. 
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surface area

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

Ex: To find the surface area of a cube, you calculate the area of one face and multiply it by six. 
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transversal
transversal
[Adjective]

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

Ex: In geometry, a transversal line can create various angles with the lines it intersects. 
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quadrant
quadrant
[noun]

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

Ex: Each quadrant of a circle represents one-fourth of the circle's area. 
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asymptote
asymptote
[noun]

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

Ex: The hyperbola has asymptotes that represent the lines the curve approaches but never crosses. 
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to bisect
to bisect
[Verb]

to divide something into two equal parts

Ex: Using a ruler, she carefully bisected the line on the paper. 
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tangent
tangent
[noun]

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

Ex: In geometry class, we learned how to draw a tangent to a circle, ensuring it only touched the circle at a single point. 
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chord
chord
[noun]

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

Ex: The longest chord in a circle is its diameter. 
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to translate

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

Ex: To translate the triangle 5 units to the right and 3 units up, you add 5 to the x-coordinates and 3 to the y-coordinates of each vertex. 
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