1. definitions 2. segments and lines 3. triangles 4. polygons and circles 5. 2d perimeter/area and...
TRANSCRIPT
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