Geometry
Reflection of a Figure (The Flip)
- A Reflection changes the orientation of the figure - A Reflection is an isometry
Polygon
A 2 dimensional figure which is formed by a number of line segments, each connected end to end to form a closed shape.
Right Circular Cone
A cone is a solid that has a circular base and a a single vertex. If the vertex is over the center of the base, it is called a right cone. If it is not, it is called an oblique cone.
Right Circular Cylinder
A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
Dilation of a figure
A dilation is a transformation that produces an image that is the similar to the pre-image (original figure). A dilation stretches or shrinks the pre-image. The description of a dilation includes the scale factor (or ratio) and the center of the dilation.
Special Quadrilateral
A four-sided polygon.
Net
A net is a two dimensional figure that can be folded to make a three dimensional object.
Supplementary Angle Pairs
A pair of angles whose sum is 180 degrees
Complementary Angle Pairs
A pair of angles whose sum is 90 degrees
Rhombus
A parallelogram with all congruent sides The diagonals bisect opposite angles The diagonals are perpendicular bisectors
Square
A parallelogram with four congruent sides and four congruent angles The diagonals are congruent The diagonals are perpendicular bisectors
Coordinate Plane
A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.
Center of Dilation
A point about which the figure is dilated.
Convex Polygon
A polygon that has all interior angles measure less than 180°. (All the vertices point 'outwards')
Regular Polygon
A polygon with all angles Congruent and all sides congruent.
Concave Polygon
A polygon with one or more interior angles greater than 180°. It looks like a vertex has been 'pushed in' towards the inside of the polygon.
Irregular Polygon
A polygon with sides that are not all congruent or angles that are not all congruent
Polyhedron
A polyhedron is a three-dimensional solid figure in which each side is a flat surface. These flat surfaces are polygons and are joined at their edges. The word polyhedron is derived from the Greek poly (meaning many) and the Indo-European hedron (meaning seat or face).
Proportion
A proportion is an equation with a ratio (fraction) on each side.
Trapezoid
A quadrilateral with exactly one pair of parallel sides.
Radical Expression
A radical expression is defined as any expression containing a radical (√) symbol.
Square Roots and Perfect Squares Chart
A square root is a number that, when multiplied by itself, will result in a given number.
Right Square Pyramid
A three dimensional shape that has a square base and four congruent faces that meet at a point above the base called the vertex. The vertical height (h) is the perpendicular distance from the top down to the base. The 4 lateral faces are congruent isosceles triangles. The slant height (l) is the height of the lateral faces. s is the side of the base (square).
Vertical Line
A vertical line is a line that goes straight up and down, parallel to the y-axis of the coordinate plane. All points on the line will have the same x-coordinate. The slope of a vertical line is undefined.
Classify Angles
Acute Obtuse Right Straight Reflex
Alternate Exterior Angle Pairs
Alternate Exterior Angle pairs are congruent.
Opposite Angles
Angels that do not share a side.
Angle Bisector
Angle bisector divides an angle into two congruent angles.
Circle - Chord
Chord: A line segment with the endpoint on the circumference of the circle. Diameter: A cord that passes through the center of the circle.
Concentric circles
Circles that have their centers at the same point.
Irregular Shape
Irregular shapes have sides and angles of any length and size.
Naming Angles
Name an angle in four different ways: <ABC, <CBA, <1, <B
Coordinates of a point
Point (-3, 2)
Circle (Radius, Diameter, Circumference)
Radius is the distance from the center to the edge. Diameter starts at one side of the circle, goes through the center and ends on the other side. Circumference is the distance around the edge of the circle.
Similarity Ratio
Ratio of corresponding sides
Clockwise Rotation
Right Turn
Alternate Interior Angle Pairs
Same Side Exterior Angle Pairs are supplementary (add up to 180 degrees).
Same Side Interior Angle Pairs
Same Side Interior angle pairs are supplementary (add up to 180 degrees).
Special Right Triangle 30-60-90
Short Leg is opposite the smallest angle (30°). Long Leg is opposite the 60° angle. Long Leg = (short leg) *√3. Hypotenuse = 2 * Short Leg
Slope is Negative
Slope drops from left to right
Slope is Zero
Slope of a Horizontal Line Equation of a horizontal line y=constant Examples: y=3, y=-4
Slope is Positive
Slope rises from left to right
Special Right Triangles
Special Right Triangle are right triangles 1. Special Right Triangle 45º- 45º- 90º 2. Special Right Triangle 30º- 60º- 90º
Sphere
Surface Area: The number of square units that will exactly cover the surface of a sphere. Volume: The number of cubic units that will exactly fill a sphere.
Scale Factor
The amount by which the image grows or shrinks is called the "Scale Factor". SF > 1 --> Image is enlarged (larger) 0 < SF < 1 --> Image is reduced (smaller) SF = 1 --> Image is the exact same size as the original (Isometry).
Midpoint Formula
The coordinates of the midpoint of a line segment are the average of the coordinates of its endpoints.
Circle - Measure of Major Arc
The measure of a major arc equals 360 minus the measure of the minor arc.
Circle - Measure of Minor Arc
The measure of a minor arc equals the measure of its central angle.
Circle - Measure of Minor and Major Arcs
The measure of an arc is equal to the measure of the central angle. Measure of Minor Arc < 180 degrees Measure of Major Arc > 180 degrees
Triangle Exterior Angle Theorem
The measure of an exterior angle is equal to the sum of the two remote interior angles.
Central Angle Theorem
The measure of the inscribed angle (∠ABC) is always half the measure of the central angle (∠AOC) when both angles intercept the same arc AC.
Midpoint of a Line Segment
The midpoint is equidistant from the endpoints.
Circle - Area of Sector
The number of square units it takes to exactly fill a sector of a circle.
Midpoint Definition
The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal segments. By definition, a midpoint of a line segment is the point on that line segment that divides the segment two congruent segments.
Slant Height of a Cone
The slant height is the distance from the vertex of the cone, down the side, to a point on the circumference of the base.
Slant height of a pyramid
The slant height is used to find the total surface area of a pyramid. The slant height is not the height of the pyramid.
Slope
The steepness of a line on a graph Rise over Run
Triangle Angle Sum Theorem
The sum of the three angle measures of any triangle is always180 degrees..
Transformation Image
The transformed figure
Three Dimensional Shapes or Solids
Three-Dimensional shapes can be made up of flat of curved or flat surfaces
Simplify Square Roots
To simplify a square root, you "take out" anything that is a "perfect square".
Solving a Proportion
To solve a proportion, cross multiple and solve the equation for the unknown.
Surface Area Cylinder
Total SA = LA + Area of 2 Bases
Transformation of a figure
Transformation is a change in position, shape, or size of a figure.
Perpendicular Lines
Two line that intersect at 90 degree angles.
Consecutive Sides
Two sides of a polygon with a common vertex.
Volume cylinder
Volume is the number of cubic units to exactly fill a Cylinder.
Volume of Rectangular Prism
Volume is the number of cubic units to exactly fill a prism.
Radical Expressions and how to Rationalize the Denominator
When you have a fraction with a radical in the denominator, you can use a technique called rationalizing a denominator to eliminate the radical. Multiply numerator and denominator by the radical that converts the denominator into a square root of a perfect square.
Pythagorean Triples
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
Composite figure
A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape).
Horizontal Line
A horizontal line is one the goes left-to-right, parallel to the x-axis of the coordinate plane. All points on the line will have the same y-coordinate. A horizontal line has a slope of zero.
Tangent
A line that "just touches" the circle at one point.
Transversal line
A line that cuts across parallel lines at two distinct points.
Rectangle
A parallelogram with four right angles The diagonals are congruent and bisect each other
Ratio
A ratio is a comparison of two numbers. It is expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second.
Rotation of a figure (Turn)
A rotation is a transformation where a figure is turned about a given point (center of rotation). A Rotation is an isometry.
Circle - Sector
A sector is a region bounded by two radii of a circle and the intercepted arc of the circle.
Right Rectangular Prism
A solid (3-dimensional) object which has six faces that are rectangles. The two bases are parallel and congruent. It has the same cross-section along a length, which makes it a prism.
Isosceles Trapezoid
A trapezoid with congruent legs
Sum of Exterior Angles of a Polygon
Always equals 360 degrees
Angle
An Angle is a figure formed by two rays (called SIDES or LEGS) with a common endpoint called the VERTEX (plural VERTICES).
Central Angle
An angle formed at the center of a circle by two radii. The vertex of a central angle is always the center of the circle. The measure of a central angle is equal the measure of the intercepted arc.
Exterior Angle
An angle formed by one side of a polygon and the extension of an adjacent side
Interior Angle
An angle inside a polygon
Inscribed Angle
An angle is inscribed in a circle if the vertex of the angle is on the circle and the sides of the angle are chords of the circle
Consecutive or Adjacent Angles
Angles of a polygon that share a common side.
Area vs perimeter
Area is the number of square units enclosed by the 2D shape. Perimeter is the distance around the outside of a 2D shape.
Area
Area is the number of square units enclosed by the two dimensional shape.
Parallelogram
Both pairs of opposite sides are parallel and congruent Opposite angles are congruent Consecutive angles are supplementary The diagonals bisect each other
Classify Triangles
By Angles: Acute, Obtuse, Right, Equiangular By Sides: Equilateral, Isosceles, Scalene
Special quadrilaterals Chart
Categorize special quadrilaterals according to their properties.
Corresponding Angle Pairs
Corresponding angle pairs are congruent
Congruent Polygons
Corresponding angles (matching) are congruent . Corresponding sides are congruent.
Line Segment
Distance between two endpoints
Distance between two Points in the Coordinate Plane
Distance formula
Face, Vertex, Edge
Each flat surface is called a FACE. EDGE is a line segment that is the intersection of two faces. VERTEX is the point that is the intersection of three or more faces.
Volume of Composite 3D shapes
First calculate the volume of each of individual figures and then find the volume of the entire composite figure.
Equations of horizontal and vertical lines
Graph horizontal line: y=3, y=-4, etc Graph vertical libe: x=3, x=-7 etc
Hemisphere
Half a Sphere
Pythagorean Theorem
In mathematics, the Pythagorean theorem is a relation among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Triangle angles
Interior and exterior angles
Intersecting Lines
Intersecting lines intersect at one point.
Lateral Surface Area of a Rectangular Prism
Lateral surface area (LA) is the sum of the side faces.
Counterclockwise Rotation
Left Turn
Kite
No parallel sides Two pairs of adjacent sides are congruent Exactly one pair of opposite angles are congruent The diagonals meet at a right angle
Polygon Angle Sum Theorem
Number of triangles x 180 OR (n-2)180, n = number of sides (n-2)180
Parallel Lines
Parallel lines do not intersect. They have no common point.
Circle - Arc
Part of the circumference of the circle
Circle - Arc Length
Part of the circumference of the circle.
Perimeter
Perimeter is the distance around the outside of a 2D shape.
Similar Polygons
Polygons are similar when their corresponding angles are congruent and the ration of their corresponding sides are in proportion.
Special Right Triangle 45-45-90
Right Isosceles triangle. Both legs are equal. Hypotenuse= Leg * √ 2
Slope is Undefined
Slope of a Vertical Line. Equation of a vertical line x=constant Examples: x=3, x=-4
Circle - Measure of a Semicircle
The measure of a a semicircle equals 180 degrees.
Pre-image
The original figure
Comparing Ratios (Fractions)
The ratios are equal if their cross products are equal.
Volume Comparison: Cylinder and Cone
The volume of a cone is 1/3 the volume of a cylinder that has the same height and the same base.
Volume of a Cone
The volume of a cone is 1/3 the volume of a cylinder that has the same height and the same base.
Total Surface Area of Rectangular Prism
Total SA = LA + Areas of 2 Bases A right prism has a set of flat surfaces called the FACES. Total Surface Area (SA) is the sum of all faces. The two bases (top and bottom faces) are parallel and congruent.
Isometry
Transformation of a figure in which the pre-image of a figure and the image of the figure are congruent.
Translation of a Figure (sliding motion)
Translation is a transformation that moves points the same distance and in the same direction. - A Translation DOES NOT change the orientation of the figure. - A Translation is an isometry. Example: (x-7, y-3) algebraic notation or <-7,-3> vector notation
Trapezoid
Two dimensional shape with four sides and one pair of parallel and congruent sides.
Distance between two Points in the Coordinate Plane using the Pythagorean Theorem
Use the Pythagorean Theorem on the coordinate plane.
Vertical Angle Pair
Vertical angle pairs are congruent. They are formed by two intersecting lines.