Download SAT Math Power Point Week 3

1.
2.
3.
4.
5.
Definitions
Segments and Lines
Triangles
Polygons and Circles
2D Perimeter/Area and 3D Volume/Surface Area
 Lines extends indefinitely
 Segments are portions of lines that starts at a point and end at







another points. These are called Endpoints
Rays starts at a point and extends indefinitely in one direction
Things that are “Congruent” are equaled in measurement
Angles are the space in-between two connected rays that is
usually measured in Degrees
Vertical Angles are two opposite angles formed by two
intersecting lines. Vertical angles are also congruent
Complementary 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
 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)
𝑥1 + 𝑥2 𝑦1 + 𝑦2
,
2
2
 Distance Formula
𝑑=
𝑥22 − 𝑥12 + 𝑦22 − 𝑦12
 Example:
Given (5, 3) , (-4, y) and a distance of 5.
Find the midpoint
 Slopes in Geometry is the same as in Algebra
 Parallel lines have the same slope

a b
e f
i j
m n
c d
g h
k l
o p
 Triangle Sum Theorem: The sum of all the angles within a
triangle is equal to 1800
 Types of Triangles by Sides
Equilateral – All sides of a triangle have the same length
Isosceles – Exactly two sides of a triangle have the same
length
Scalene – All sides of the triangle have different length
 Types of Triangles by Angle
Acute – 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
 Triangle Inequality states that the sum of any two sides
must always be greater than the third side
 Pythagorean Theorem
If 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
a
c
b
Then we have the equation
𝑎2 + 𝑏 2 = 𝑐 2
 Special Right Triangles

45-45-90
30-60-90
 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
 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 includes
Triangle, Quadrilaterals, Pentagon, Hexagon,
Heptagon, Octagon, Nonagon, and Decagon
Examples of Quadrilaterals include
Parallelograms, Rhombus, Rectangle, Square, Kite
Keep in mind that all regular polygons can be broken
up into triangles
 Circles are perfectly round shapes
 Diameter 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
 Perimeter is the distance around a shape





In particular for a quadrilateral, the formula is 2l + 2w
Area is the flat space a shape can hold
Volume is the space a solid can hold
Surface area is the sum of all the areas of a solid
Solids include Prisms, Cylinders, Pyramids and Spheres
All formulas for area, volume, and surface area are on
the first page of each section