Unit 1: Points, Lines, and Planes

Source: Topic 1, Day 1 Notes

Point

A location in space with no size or dimension

Line (Straight)

Set of infinite points in opposite direction; 1D

Plane

Flat surface that extends without an end; 2D

Collinear

Points that lie on the same line

Coplanar

Points and lines that lie on the same plane

Line Segment/Segment

PART of a line, includes two endpoints and all points in between; typically 2 points together only

Ray

PART of a line, includes an endpoint and all points in between to the other side of the ray

Opposite Rays

Two rays that share the same endpoint AND form a 180 DEGREES LINE

Angles

Formed by two noncollinear rays with a common endpoint (VERTEX); rays are the sides or “legs” of angle

Postulate or Axioms

They mean the SAME thing: accepted facts without proofs

Theorem

Proven to be true “proofs”

Segment Addition POSTULATE

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

Angle Addition POSTULATE

If point D is in the INTERIOR angle of <ABC, then m<ABD + m<DBC = m<ABC

Congruent Segments

Numerical expressions have same NUMERICAL VALUE, then they’re equal (=). If two segments have the same LENGTH, they are congruent (≅)

Midpoints

Midpoint of a segment is a point that divides the segment into two CONGRUENT segments

Segment Bisector

A point, line, or other segment that intersects a segment at its midpoint and bisects that segment

Congruent Angles

Two angles are congruent ONLY IF they have the same MEASURE

Angle Bisector

A ray that divides an angle into two CONGRUENT angles