SAT Math and Logic - Geometry

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 steeper the slope , the larger the value when you calculate rise over run .

arc [noun]

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

Ex: In a pie chart , each section can be represented by an arc of the circle .

angle [noun]

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

Ex: The angle between the two roads created a sharp turn that drivers needed to navigate carefully .

radian [noun]

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

Ex: The unit circle helps visualize angles measured in radians .

right angle [noun]

an angle measuring exactly 90 degrees

Ex: The painter meticulously ensured that the lines on the canvas formed right angles to create a sense of balance in the composition .

acute angle [noun]

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

vertical angle [noun]

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

Ex: In the diagram , angle A and angle B are vertical angles and thus have the same measure .

consecutive angle [noun]

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

Ex: When drawing a hexagon , you can see that each pair of consecutive angles shares a common side .

polygon [noun]

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

Ex: The stop sign is an example of an octagonal polygon .

parallelogram [noun]

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

quadrilateral [noun]

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

hyperbola [noun]

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

Ex: The distance between a point on the hyperbola and its two foci is constant , defining its geometric properties .

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: Designers use parabolas to create efficient lighting fixtures .

rhombus [noun]

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

pentagon [noun]

a geometric shape with five angles and five straight sides

Ex: The stop sign is shaped like a red pentagon to alert drivers to halt .

tetrahedron [noun]

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

trapezoid [noun]

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

equilateral triangle [noun]

a type of triangle with all three sides of equal length

Ex: The fence surrounding the garden formed an equilateral triangle at each corner .

right triangle [noun]

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

acute triangle [noun]

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

Ex: An equilateral triangle is always an acute triangle since all its angles are 60 degrees .

isosceles triangle [noun]

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

Ex: The altitude drawn from the vertex angle of an isosceles triangle bisects the base into two equal segments .

scalene triangle [noun]

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

Ex: The bridge 's supports created a scalene triangle pattern against the skyline .

obtuse triangle [noun]

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

Ex: When drawing an obtuse triangle , ensure one angle is larger than 90 degrees while the other two are less .

rectangular pyramid [noun]

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

Ex: To find the surface area of a rectangular pyramid , you need to add the area of the rectangular base and the areas of the four triangular faces .

right circular cylinder [noun]

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

Ex: In the experiment , we filled a right circular cylinder with water to measure its capacity .

right circular cone [noun]

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

Ex: The height of a right circular cone is the perpendicular distance from the vertex to the center of the base .

epicycle [noun]

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

Ex: The geometric properties of an epicycle can be explored by examining the resulting curves and paths generated by its motion .

hypotenuse [noun]

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: A ladder leaning against a wall forms a right triangle , with the hypotenuse representing the ladder 's length .

base [noun]

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

Ex:

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 engineer measured the diameter of the pipe to ensure it would fit snugly within the existing framework .

radius [noun]

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

Ex: The architect calculated the radius of the dome to ensure its proportions were aesthetically pleasing .

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: The meeting point of the two arms of an angle is referred to as the vertex of the angle .

perimeter [noun]

the total length of the external boundary of something

Ex: The farmer used a long measuring tape to determine the perimeter of his rectangular cornfield before installing a new fence .

circumference [noun]

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

Ex: To find the circumference of a wheel , you need to know its radius or diameter .

area [noun]

the measurement of a piece of land or a flat surface

Ex: The area of a piece of land is important for property valuation .

surface area [noun]

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

Ex: Architects must consider the surface area of materials needed to cover a building .

volume [noun]

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

Ex: Engineers calculated the volume of the water tank to ensure it could hold enough water for the community .

asymptote [noun]

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

Ex: A horizontal asymptote occurs when the values of a function approach a constant as the input goes to positive or negative infinity .

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 .

protractor [noun]

a measuring instrument used to measure and draw angles

Ex: The protractor helped the student draw precise angles for the math assignment .

line of symmetry [noun]

a line that divides a shape into two congruent parts

Ex: A square has four lines of symmetry : two along its diagonals and two along the midlines parallel to its sides .

geometric series [noun]

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: Convergence of a geometric series occurs when the absolute value of the common ratio is less than 1 .

quadrant [noun]

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

Ex: In a pie chart , each section can be divided into quadrants for detailed analysis .

interior angle [noun]

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

Ex: The interior angles of a quadrilateral add up to 360 degrees .

ellipse [noun]

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

chord [noun]

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

Ex: Any chord divides the circle into two arcs .

diagonal [adjective]

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

Ex: The diagonal plane of the cube divided it into two symmetrical halves .

congruent [adjective]

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

Ex:

parallel [adjective]

having an equal distance from each other at every point

Ex: The beams of sunlight created parallel lines on the floor .

transversal [adjective]

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

Ex: The researcher analyzed the complex dynamics of the system , focusing on the transversal heteroclinic connections between saddle points in the phase space .

perpendicular [adjective]

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

Ex: The engineer emphasized the importance of installing perpendicular supports for the ceiling .

to bisect [verb]

to divide something into two equal parts

Ex: The chef demonstrated how to bisect the cake to achieve identical slices .

to translate [verb]

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

Ex: The transformation matrix can be used to translate a point by a specified vector .

asymmetry [noun]

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

Ex: The artist used asymmetry to create an interesting visual effect .

SAT Math and Logic
Mathematics	Arithmetic and Statistics	Geometry	Time and Order
Quantity and Partitives	Finance	Inclusion and Characterization	Comparison
Certainty and Uncertainty	Regularity and Rationality	Irregularity and Irrationality	Causality and Intentionality
Praise	Evaluation and Criticism	Importance	Research and Innovation