SAT MATH PREP WEEK 3

1. Definitions 2. Segments and Lines3. Triangles4. Polygons and Circles5. 2D Perimeter/Area and 3D Volume/Surface

Area

Today’s Topic - Geometry

Lines extends indefinitelySegments are portions of lines that starts at a point and end

at another points. These are called EndpointsRays starts at a point and extends indefinitely in one directionThings that are “Congruent” are equaled in measurementAngles are the space in-between two connected rays that is

usually measured in DegreesVertical Angles are two opposite angles formed by two

intersecting lines. Vertical angles are also congruentComplementary Angles are two angles whose sum is 900

Supplementary Angles are two angles whose sum is 1800

A Linear Pair are pairs of connected angles that form a straight line and are also supplementary angles

Definitions I

The Segment Addition Postulate proposed that if two segments are put together, they form a bigger segment

Example:The measure of AB is 2 and the measure of AC is 5. What is the measure of BC?

Midpoint formula:Given points (x1, y1) and (x2, y2)

Segment Addition Postulate ,Distance, & Mid Point Formula I

Distance Formula

Example:Given (5, 3) , (-4, y) and a distance of 5. Find the midpoint

Segment Addition Postulate ,Distance, & Mid Point Formula II

Slopes in Geometry is the same as in AlgebraParallel lines have the same slope

a b c d e f g h

i j k lm n o p

Parallel Lines

Triangle Sum Theorem: The sum of all the angles within a triangle is equal to 1800

Types of Triangles by SidesEquilateral – All sides of a triangle have the same lengthIsosceles – Exactly two sides of a triangle have the same lengthScalene – All sides of the triangle have different length

Types of Triangles by AngleAcute – All angles in the triangle have a measure of less than 900

Obtuse – Exactly one angle in a triangle has a measure of more than 900

Right – Exactly one angle in a triangle has a measure of 900

Triangles I

Triangle Inequality states that the sum of any two sides must always be greater than the third side

Pythagorean TheoremIf a triangle is a right triangle, the sum of the squared length of two the sides is equaled to the length of the third side squared.

If a right triangle is labeled as followed

c a

bThen we have the equation

Triangle II

Special Right Triangles 45-45-90 30-60-90

Triangle III

Two Triangles are congruent if they satisfy the conditions in one of the following:SSS, SAS, AAS, ASA, Leg-Hypotenuse

Two Triangle are similar if all the ratios between corresponding parts of the triangles are the same

Triangle IV

Polygons are shapes with 3 or more straight sides and angles

Interior Angle Sum on a polygon is defined by 180(n-2)Where n is the number of sides

A couple of Polygons includesTriangle, Quadrilaterals, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, and Decagon

Examples of Quadrilaterals includeParallelograms, Rhombus, Rectangle, Square, Kite

Keep in mind that all regular polygons can be broken up into triangles

Polygons

Circles are perfectly round shapesDiameter is any line drawn from one end of a

circle to the other end that must pass through the center

Radius is the any line drawn from the center to one end of a circle

Chords are any line drawn from one end of a circle to another end that doesn’t pass through the center

Circumference of a circle is the distance around the circle defined as C = 2πr

Arc length is a portion of the circumference

Circle

Perimeter is the distance around a shapeIn particular for a quadrilateral, the formula is 2l + 2w

Area is the flat space a shape can holdVolume is the space a solid can holdSurface area is the sum of all the areas of a

solidSolids include Prisms, Cylinders, Pyramids

and SpheresAll formulas for area, volume, and surface

area are on the first page of each section

2D Perimeter/Area and 3D Volume/Surface Area