673: GEOMETRY - created from Mind Map

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Points, Lines, Planes, Angles

Perpendicular and Parallel Lines

Logical Reasoning

Attributes/Properties of Triangles

Quadrilaterals

Transformations

Similarity

Circles

3D Figures

Distance

Midpoint

Line seg AM = Line seg MB

4x - 6 = 2x + 10

2x = 16

x = 8

Line seg AM = 4(8) - 6 = 26

Line seg AB = 26(2) = 52

Types of Angles

Using coordinates (x1, y1) and (x2, y2) d =√(x2 - x1)^2 + (y2-y1)^2

complementary

2x + 25 + x + 5 = 90

3x + 30 = 90

3x = 60

x = 20

supplementary

Vertical

Adjacent

Parallel lines cut by a transversal

Relationship of slopes

alternate interior angles

same-side interior angles

alternate exterior angles

2x -10 = 110

2x = 120

x = 60

if lines are parallel, slopes are same

if lines are perpendicular, slopes are opposite reciprocals

deductive reasoning

formal proofs

counter-example

use when proving a conjecture false!

inductive reasoning

find patterns, make conjectures

conjecture

proofs

writing proofs, paragraphs proofs, two-column proofs

conditional statement

use to draw valid conclusions

Properties!

converse, contrapositive, inverse

determine if true or false

hypothesis

Law of detachment

Law of detachment is used when you have a conditional statement and another statement that matches the hypothesis (the part following if) of the conditional. The conclusion is the conclusion (second part) of the conditional. 1. If p, then q 2. p -- Therefore, q

Syllogism

Law of syllogism is used when you have two conditionals and the hypothesis of one matches the conclusion of the other. If p, then q If q, then r -- Therefore if p, then r

reflexive

The reflexive property of equality simply states that a value is equal to itself. Further, this property states that for all real numbers, x = x.

symmetric

The Symmetric Property states that for all real numbers x and y,

if x=y , then y=x .

transitive

The Transitive Property states that for all real numbers x, y, and z,

if x=y and y=z , then x=z .

triangle congruency with SSS, SAD, ASA, AAS

equilateral, isoscele, scalene, right, obtuse, acute, equiangular

Pythagorean theorem with right triangles!

180 degrees

x + 102 + 51 = 180

x + 153 = 180

x = 27 degrees

trig!!!

30, 60, 90 and 45, 45, 90

sine, cosine, tangents (SOH CAH TOA)

polygon

parallelogram, rhombus, rectangle, square, trapezoid, kite

reflection (isometry), translation (isometry), rotation (isometry) (angle of rotation), dilation (scale factor)

line of reflection, center of rotation, center of dilation

cross product property

5 (x) = 7 (x - 2)

5x = 7x - 14

-2x = -14

x = 7

geometric means

proportionality theorems

chord, secant, trangent, minor arc, major arc

diameter, radius

inscribed angle, intercepted arc, circumscribed

volume

face

lateral area

prism, pyramid, cylinder, cone, sphere

nets!!

Flattened out 3D firgure

The net to the left is a triangular pyramid (A)

base

slant height/height