Unit 1 by kei oh

Vocabulary \(^o^)/

broken1004 — 2015-09-09 19:51:10 UTC

Point

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A dot that represents a location on a plane or in space

Line

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Perfectly straight, contain an infinite number of points, extend infinitely in to directions, and have no thickness

Plane

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A flat surface that extends infinitely in all directions

Line Segment

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A part of a line that begins at one point and ends at another

Postulates & Theorems \(^o^)/

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Ray

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A part of a line that starts at one point and extends infinitely in one direction

Opposite Rays

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Rays with a common endpoint, extending in opposite directions and forming a line

Endpoint

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A point at an end of a segment or the starting point of a ray

Collinear

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Lying on the same line

Coplanar

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Lying on the same plane

Angle

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A figure formed by two rays with a common endpoint

Vertex

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A point where the edges of a figure intersect

Acute Angle

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An angle whose measure is less than 90º

Right Angle

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An angle with a measure of 90º

Obtuse Angle

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An angle whose measure is greater than 90º and less than 180º

Straight Angle

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An angle with a measure of 180º

Reflex Angle

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Angles with measures greater than 180º

Adjacent Angle

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Two angles in a plane that share a common vertex and a common side but have no interior points in common

Congruent

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The relationship between figures having the same shape and size

Compass

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An instrument with two arms, one sharp and one with a pencil that can be used to draw circles or arcs

Straight Edge

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An idealized mathematical object having a rigorously straight edge which can be used to draw a line segment

Parallel Lines

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Same distance apart (equidistant) and will never meet

Perpendicular Lines

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Lines that intersect to form right angles

Bisect

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To divide into two equal parts

Bisector

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The line that divides something into two equal parts

Midpoint

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The middle of. The point halfway along

Circle

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The set of points in a plane that are equidistant from a given point known as the center of the circle

Arc of a Circle

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Part of the circumference of a circle

Postulate

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The intersection of two lines is a point

Postulate

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The intersection of two planes is a line

Postulate

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Through any two points there is exactly one line

Postulate

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If two points are in a plane, then the line containing them is in the plane

Segment Addition Postulate

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If point R is between points P and Q on a line, then

PR + RQ = PQ

Angle Addition Postulate

broken1004 — 2015-09-10 03:43:32 UTC

If point S is in the interior of ∠PQR, then

m∠PQS + m∠SQR = m∠PQR

The Parallel Postulate

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Given a line and a point not on the line, there is one and only one line that contains the given point and is parallel to the given line

Postulate

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A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane

Postulate

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Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane

Theorem

broken1004 — 2015-09-10 18:58:43 UTC

Through a line and a point not on the line there is exactly one plane

Theorem

broken1004 — 2015-09-10 18:59:25 UTC

If two lines intersect, then exactly one plane contains the lines

Midpoint Theorem

broken1004 — 2015-09-10 19:01:21 UTC

If M is the midpoint of (line segment) AB, then AM = 1/2AB and MB =1/2AB

Angle Bisector Theorem

broken1004 — 2015-09-10 19:04:42 UTC

If (ray) BX is the bisector of ∠ABC, then m∠ABX = 1/2m ∠ABC and m∠XBC = 1/2∠ABC

Theorem

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If two lines are perpendicular, then they form congruent adjacent angles

Constructions \(^o^)/

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Copy a Segment

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https://www.youtube.com/watch?v=dUhOILbpYq4

Copy an Angle

broken1004 — 2015-09-10 19:21:10 UTC

https://www.youtube.com/watch?v=agL9WVapsnM

Bisect a Segment

broken1004 — 2015-09-10 19:21:31 UTC

https://www.youtube.com/watch?v=QAMOFWrKEUA

Bisect an Angle

broken1004 — 2015-09-10 19:21:58 UTC

https://www.youtube.com/watch?v=2lP1NKYLKQw

Perpendicularly Bisect a Segment

broken1004 — 2015-09-10 19:22:07 UTC

https://www.khanacademy.org/math/geometry/geometric-constructions/geo-bisectors/v/constructing-a-perpendicular-bisector-using-a-compass-and-straightedge

Construct a Line Parallel to a Given Line through a Point Not on the Given Line

broken1004 — 2015-09-10 19:22:51 UTC

https://www.youtube.com/watch?v=im81vHIhZS8

Mind Map \(^o^)/

broken1004 — 2015-09-10 19:23:11 UTC

broken1004 — 2015-09-10 23:57:30 UTC