Points, Lines and Planes Point (A): Any location in space

Line ( AB, l ): No width, series of points extending in either direction without end

Ray ( AB ): All points starting with initial point (A) and continuing without end in towards (B)

Segment ( AB ): All points between and including endpoints A and B.

Plane (ABC, M): All points extending in two directions.

Segments Segment addition:

AB + BC = AC

Length (distance) A(Xa, Ya) to B (Xb, Yb)

d = AB = √ (Xb - Xa)2 + (Yb - Ya)2

Midpoint A(Xa, Ya) to B (Xb, Yb)

(XM, YM) = (Xa + Xb) , (Ya + Yb)

2 2

A B C

Reverse Midpoint Steps

Stack the known Endpoint over the Midpoint

Find the change in X and Y to get from the Endpoint to the midpoint.

Repeat that change to the midpoint to get the other endpoint

A ( 2, 4 )

M ( 1, 10) {Pattern: change X by -1, change Y by +6}

B (1 + (-1), 10 + 6 ) = (0, 16)

Angles Angle Addition Postulate

m<1 + m<2 = m<AVC1

2

V C

A

B

Bisectors VB bisects <AVC

m<1 = m<2

M is the midpoint of AB

AM = MC

12

V C

A

B

A M C

Special Angle Relationships

Area and PerimeterFigure Area Perimeter

Square bh = s2 4s

Rectangle lw 2(l+w)

Parallelogram bh add the 4 sides

Trapezoid ½ (b1 + b2) h add the 4 sides

Triangle ½bh add the 3 sides

Circle π r2 2 π r = π d

May need the Pythagorean Theorem: a2 + b2 = c2

ca

b