Geometry basics
65 flashcards covering Geometry basics for the SAT Math section.
Geometry basics are the foundational concepts in math that deal with shapes, sizes, and spatial relationships. At its core, it involves studying points, lines, angles, and two- and three-dimensional figures like triangles, circles, and polygons. You'll learn how to measure lengths, areas, volumes, and angles, as well as work with coordinates on a plane. These ideas help you visualize and solve problems in everyday contexts, from designing structures to navigating maps.
On the SAT Math section, geometry questions often appear in multiple-choice formats, testing skills like calculating areas and perimeters, identifying similar shapes, or applying theorems such as the Pythagorean theorem. Common traps include misinterpreting diagrams that aren't drawn to scale or forgetting to consider all angle relationships. Focus on mastering formulas for common shapes and practicing problem-solving with visual aids to avoid errors.
A helpful tip: Always label your diagrams clearly when working through problems.
Terms (65)
- 01
Point
A point is a specific location in space that has no dimensions, such as length, width, or height, and is often represented by a dot.
- 02
Line
A line is a straight one-dimensional figure that extends infinitely in both directions and consists of an infinite number of points.
- 03
Line segment
A line segment is a part of a line that is bounded by two distinct endpoints and has a definite length.
- 04
Ray
A ray is a part of a line that starts at a specific point and extends infinitely in one direction.
- 05
Angle
An angle is formed by two rays that share a common endpoint, called the vertex, and is measured in degrees.
- 06
Acute angle
An acute angle is an angle that measures less than 90 degrees.
- 07
Right angle
A right angle is an angle that measures exactly 90 degrees and is often represented by a square symbol.
- 08
Obtuse angle
An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.
- 09
Straight angle
A straight angle is an angle that measures exactly 180 degrees and forms a straight line.
- 10
Parallel lines
Parallel lines are lines in a plane that never intersect and are always the same distance apart.
- 11
Perpendicular lines
Perpendicular lines are lines that intersect at a right angle, forming 90-degree angles at the point of intersection.
- 12
Triangle
A triangle is a polygon with three sides and three angles, and the sum of its interior angles is always 180 degrees.
- 13
Equilateral triangle
An equilateral triangle is a triangle where all three sides are equal in length and all three angles measure 60 degrees.
- 14
Isosceles triangle
An isosceles triangle is a triangle with at least two sides of equal length, and the angles opposite those sides are also equal.
- 15
Scalene triangle
A scalene triangle is a triangle where all three sides are of different lengths, and all three angles are of different measures.
- 16
Right triangle
A right triangle is a triangle that has one angle measuring exactly 90 degrees, and it follows the Pythagorean theorem.
- 17
Acute triangle
An acute triangle is a triangle where all three interior angles are less than 90 degrees.
- 18
Obtuse triangle
An obtuse triangle is a triangle that has one interior angle greater than 90 degrees and two angles less than 90 degrees.
- 19
Pythagorean theorem
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
- 20
Area of a triangle
The area of a triangle is calculated using the formula one-half times base times height, where the base and height are perpendicular.
- 21
Perimeter of a triangle
The perimeter of a triangle is the total length around the shape, found by adding the lengths of all three sides.
- 22
Quadrilateral
A quadrilateral is a polygon with four sides and four angles, and the sum of its interior angles is 360 degrees.
- 23
Square
A square is a quadrilateral with all four sides equal in length and all four angles measuring 90 degrees.
- 24
Rectangle
A rectangle is a quadrilateral with four right angles, and opposite sides are equal in length.
- 25
Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides, and opposite sides are equal in length and opposite angles are equal.
- 26
Rhombus
A rhombus is a quadrilateral with all four sides equal in length, and its diagonals bisect each other at right angles.
- 27
Trapezoid
A trapezoid is a quadrilateral with at least one pair of parallel sides, called the bases, and the non-parallel sides are the legs.
- 28
Area of a rectangle
The area of a rectangle is calculated by multiplying its length by its width.
- 29
Area of a square
The area of a square is calculated by squaring the length of one of its sides.
- 30
Area of a parallelogram
The area of a parallelogram is found by multiplying its base by its height.
- 31
Area of a trapezoid
The area of a trapezoid is calculated by averaging the lengths of the two parallel sides and multiplying by the height.
- 32
Circle
A circle is a round shape where all points on the shape are equidistant from a fixed center point.
- 33
Radius
The radius of a circle is the distance from the center to any point on the circle.
- 34
Diameter
The diameter of a circle is a straight line passing through the center and connecting two points on the circle, equal to twice the radius.
- 35
Circumference
The circumference of a circle is the distance around the circle, calculated using the formula pi times the diameter.
- 36
Area of a circle
The area of a circle is calculated using the formula pi times the radius squared.
- 37
Arc of a circle
An arc is a portion of the circumference of a circle, and its length is a fraction of the full circumference based on the central angle.
- 38
Sector of a circle
A sector is a region bounded by two radii and an arc of a circle, like a slice of pie.
- 39
Volume of a rectangular prism
The volume of a rectangular prism is calculated by multiplying its length, width, and height.
- 40
Volume of a cylinder
The volume of a cylinder is calculated by multiplying pi times the radius squared times the height.
- 41
Surface area of a rectangular prism
The surface area of a rectangular prism is the total area of all its faces, found by adding twice the area of the base and twice the area of the sides.
- 42
Coordinate plane
The coordinate plane is a two-dimensional surface formed by two perpendicular number lines, called axes, that intersect at the origin.
- 43
X-axis
The x-axis is the horizontal number line on the coordinate plane, where points are plotted based on their x-coordinates.
- 44
Y-axis
The y-axis is the vertical number line on the coordinate plane, where points are plotted based on their y-coordinates.
- 45
Origin
The origin is the point where the x-axis and y-axis intersect on the coordinate plane, with coordinates (0, 0).
- 46
Slope
Slope is a measure of the steepness of a line, calculated as the change in y-coordinates divided by the change in x-coordinates between two points.
- 47
Distance formula
The distance formula calculates the length between two points on the coordinate plane using the square root of the sum of the squared differences in their x and y coordinates.
- 48
Midpoint formula
The midpoint formula finds the coordinates of the midpoint between two points by averaging the x-coordinates and averaging the y-coordinates.
- 49
Equation of a line
The equation of a line represents its position on the coordinate plane and can be written in forms like slope-intercept or point-slope.
- 50
Slope-intercept form
Slope-intercept form is a way to write the equation of a line as y equals m x plus b, where m is the slope and b is the y-intercept.
- 51
Point-slope form
Point-slope form is a way to write the equation of a line as y minus y1 equals m times (x minus x1), using a point (x1, y1) and slope m.
- 52
Similar figures
Similar figures are shapes that have the same shape but not necessarily the same size, with corresponding angles equal and corresponding sides proportional.
- 53
Congruent figures
Congruent figures are shapes that are identical in both shape and size, meaning all corresponding sides and angles are equal.
- 54
Angle sum property of triangles
The angle sum property of triangles states that the sum of the interior angles in any triangle is always 180 degrees.
- 55
Interior angle sum of a polygon
The sum of the interior angles of a polygon with n sides is calculated as (n - 2) times 180 degrees.
- 56
Common trap: Confusing area and perimeter
A common trap is mixing up area, which is the space inside a shape, with perimeter, which is the boundary length, leading to incorrect calculations.
- 57
Strategy for solving geometry word problems
A strategy for geometry word problems is to draw a diagram, label all given information, identify the needed formula, and check units for consistency.
- 58
Example: Finding area of a triangle
For a triangle with base 5 units and height 10 units, the area is calculated as one-half times base times height, resulting in 25 square units.
Base = 5, height = 10; area = 0.5 5 10 = 25.
- 59
Pythagorean triples
Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, such as 3-4-5 or 5-12-13, useful for quick right triangle calculations.
- 60
Composite shapes
Composite shapes are figures made by combining two or more basic shapes, and their area or perimeter is found by adding or subtracting the areas of the individual parts.
- 61
Reflections in geometry
Reflections are transformations that flip a shape over a line, called the line of reflection, resulting in a mirror image of the original shape.
- 62
Rotations in geometry
Rotations are transformations that turn a shape around a fixed point by a certain angle, such as 90 or 180 degrees, preserving the shape's size and form.
- 63
Translations in geometry
Translations are transformations that slide a shape in a straight line without rotating or flipping it, moving every point by the same distance and direction.
- 64
Perimeter of composite shapes
The perimeter of composite shapes is the total length of the outer boundary, calculated by adding the lengths of the external sides and subtracting any internal ones.
- 65
Arc length
Arc length is the measure of the distance along an arc of a circle, calculated as the fraction of the circumference corresponding to the central angle.