The Building Blocks of Geometry

Geometry Chapter 1

Point

Has no size

Line

Infinitely many points, extends forever, has no thickness, perfectly straight

Plane

Flat surface that extends infinitely in all directions

Collinear

Points all on the same line

Coplanar

Points all on the same plane; name a plane by 3 non-collinear points or by a capital letter in the corner

Intersecting Lines

Two lines that cross at a point

Intersecting Planes

Two planes that intersect in a line

Segment

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

Ray

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

Measuring Segments

The distance between two points A and B is written as AB

Segment Addition

If A, B, and C are collinear and B is between A and C, then AB + BC = AC

Congruent

Equal in measure

Segment Congruence

Two segments that have the same length

Midpoint of a Segment

Point that divides a segment into two equal parts

Angle

Formed by two rays with a common endpoint (vertex)

Acute

Angle less than 90°

Obtuse

Angle greater than 90° but less than 180°

Right

Angle exactly 90°

Straight

Angle exactly 180°

How to Measure with a Protractor

Place center at vertex, align one side, read degrees where the other side crosses the scale

Angle Congruence

Two angles that have the same measure

Angle Bisector

A ray that divides an angle into two equal angles

Angle Addition Postulate

If point B is in the interior of ∠AOC, then ∠AOB + ∠BOC = ∠AOC

Adjacent Angles

Two angles that share a common side and vertex

Vertical Angles

Opposite angles formed by two intersecting lines; always congruent

Complementary Angles

Two angles whose measures add up to 90°

Supplementary Angles

Two angles whose measures add up to 180°

Linear Pair

Two adjacent angles that form a straight line

Parallel Lines

Lines in the same plane that never intersect

Perpendicular Lines

Lines that intersect at a right angle

Skew Lines

Lines that are not parallel and not in the same plane

Right Triangle

A triangle with one right angle

Acute Triangle

A triangle with all acute angles

Obtuse Triangle

A triangle with one obtuse angle

Scalene Triangle

A triangle with no equal sides

Equilateral Triangle

A triangle with all sides equal

Isosceles Triangle

A triangle with two equal sides

Perimeter

The sum of the lengths of all sides of a figure

Polygons

Closed figures with three or more straight sides

Sides

The line segments that make up a polygon

Vertices

Points where two sides of a polygon meet

Midpoint Formula

(x₁ + x₂)/2 , (y₁ + y₂)/2

Algebraic Proofs

Using algebraic properties to show statements are true