Geometry Review

Area : The number of square units enclosed by the two dimensional shape.

Perimeter : The distance around the outside of a 2-dimensional shape.

Concentric circles : Circles that have their centers at the same point.

Three Dimensional Shapes or Solids : Three-Dimensional shapes can be made up of flat of curved or flat surfaces

Lateral Surface Area of a prism or pyramid : Lateral surface area (LA) is the sum of the areas of the side faces.

Total Surface Area of Rectangular Prism : Total SA = LA + Areas of 2 BasesA 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.

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.

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.

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.

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).

Volume of Composite 3D shapes : First calculate the volume of each of individual figures and then find the volume of the entire composite figure.

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).

Supplementary Angle Pairs : A pair of angles whose sum is 180 degrees

Complementary Angle Pairs : A pair of angles whose sum is 90 degrees

Alternate Interior Angle Pairs : Same Side Exterior Angle Pairs are supplementary (add up to 180 degrees).

Alternate Exterior Angle Pairs : Alternate Exterior Angle pairs are congruent.

Parallel Lines : These lines do not intersect. They have no common point.Slopes of these lines are equal.

Intersecting Lines : Intersecting lines intersect at one point.

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.

Regular Polygon : A polygon with all angles Congruent andall sides congruent.

Exterior Angle : An angle formed by one side of a polygon and the extension of an adjacent side

Special Quadrilateral : A four-sided polygon.

Parallelogram : Both pairs of opposite sides are parallel and congruentOpposite angles are congruentConsecutive angles are supplementaryThe diagonals bisect each other

Rhombus : A parallelogram with all congruent sidesThe diagonals bisect opposite anglesThe diagonals are perpendicular bisectors

Kite : No parallel sidesTwo pairs of adjacent sides are congruentExactly one pair of opposite angles are congruentThe diagonals meet at a right angle

Slope : The steepness of a line on a graphRise over Run

Line Segment : Distance between two endpoints

Coordinates of a point : Point (-3, 2)

Congruent Polygons : Corresponding angles (matching) are congruent .Corresponding sides are congruent.

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.

Solving a Proportion : To solve a proportion, cross multiple and solve the equation for the unknown.

Transformation of a figure : Transformation is a change in position, shape, or size of a figure.

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.

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.

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.

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.

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 degreesMeasure of Major Arc > 180 degrees

Circle - Measure of Minor Arc : The measure of a minor arc equals the measure of its central angle.

Circle - Area of Sector : The number of square units it takes to exactly fill a sector of a circle.

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.

Special Right Triangle 45-45-90 : Right Isosceles triangle.Both legs are equal.Hypotenuse= Leg * √ 2

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