Undefined Terms

×  no formal definition

×  can only be represented or described

×  can also be dealt with through their properties which are taken up as postulates

Point /
Line /
Line Segment /
Ray /
Opposite Rays /
Half Lines /
Plane /

Basic Terms

Problem / Figure / Final Answer
If DT= 60, find the value of x, DS and ST / / x= 16
DS= 24
ST= 36
C is the midpoint of Segment AB. Find AC, CB, and AB / / AB= 22
AC and CB= 11
If RS= 3x+1, ST= 2x=2, and RT=64, find the values of x, RS, and ST / x= 13
RS= 40
ST= 24
If RS= 87+ 4, ST= 4y+8 and RT= 157-9, find the value of y, RS, ST and RT / Same as figure 3 / y= 7
RS= 60
ST= 36
RT= 96
If PT= 5x+3 and TQ= 7x=9, find x, PT, and TQ / / x= 6
PT and TQ= 33

Applying terms of if and then

Hypothesis / Conclusion / Reason
C-D-E / CD+ DE= CF / Betweenness
BC= CD / Segment BC is congruent to segment CD / Congruence
C is the midpoint of segment BD / Segment BC is congruent to segment CD / Midpoint
Segment AC is congruent to segment CF / AB= CF / Congruent Segment
Ray FG bisects segment BC / C is the midpoint of segment BD / Bisector
Hypothesis / Conclusion / Reason
W-A-Z / WA+ AZ= WZ / Betweenness
Segment SA is congruent to segment AY / XA= AY / Congruent Segments
A is the midpoint of segment WZ / Segment WA = segment AZ / Betweenness
Ray WZ bisects Segment XY / Segment XY is a bisector of segment WZ
Or
A is the midpoint of segment XY / Bisector

Angles

Problem / Final Answer
If m angle ABD= 50 and m angle CBD= 20, find m angle ABC / Angle ABC= 70 degrees
If m angle ABC= 85 and m angle ABD= 37, find m angle CBD / Angle CBD= 48 degrees
If m angle ABC= 85, m angle ABD= x+30 and m angle CBD= 2x+10, find m angle CBD and m angle ABD / m angle CBD= 40 degrees
m angle ABD= 45 degrees
If m angle ABD= x+25, m angle CBD= 3x-10 and m angle ABC- 75, what is m angle ABD and m angle CBD / m angle ABD= 40 degrees
m angle CBD= 35 degrees
If m angle ABC- 4x+ 40, m angle ABD= 50, and m angle CBD= 2x+ 10, find m angle CBD and m angle ABC / m angle CBD= 30 degrees
m angle ABC= 80 degrees
The m angle ABD= x+5, m angle CBD= 2x-20 and m angle ABC= 45. Find the m angle ABD and m angle CBD / m angle ABD= 25 degrees
m angle CBD= 20 degrees
The m angle CBD is less that twice the m angle ABD. If m angle ABC is 80, what is the m angle CBD / m angle CBD= 50 degrees
The measure of angle ABC and angle CBD are in ratios of 2:3. If the m angle ABC is 70, what is the measure of angle ABD? m angle CBD / m angle ABD= 28 degrees
m angle CBD= 42 degress

Applying terms on angles

Hypothesis / Conlcusion / Reason
Line XY is perpendicular to line FD / Forms four right angles / Perpendicularity
Ray FZ bisects angle XZF
Ray FZ bisects angle XZF / Angle FZN is congruent to angle XZN / Angle bisector
m angle FZN= m angle XZN / Angle FZN is congruent to angle XZN / Congruent angles
Angle XZG is congruent to angle FZY / m angle XZG= m angle FZY / Congruent angles
Line FG is the perpendicular bisector of line XY / Perpendicular bisector / Angle XZF, angle XZG, angle GZY and angle YZF are right angles
Line XY is perpendicular to line FG / Perpendicularity
Type of Angle / Figure
Complimentary Angles /
Supplementary Angles /
Adjacent Angle /
Vertical Angles /
Vertical Angles /
Linear Pair /

Convex and Concave Sets

Convex / Concave

VII. Properties

®  RPE (Reflexive)

×  m angle 1= m angle 1

×  3=3

®  SyPE (Symmetric)

×  m angle 1= m angle 2

×  m angle 2= m angle 1

®  TPE (Transitive)

×  AB= CD, CD= EF

×  AB= EF

®  APE (Addition)

×  m angle 1= m angle 2; m angle 3= m angle 4

×  m angle 1 + m angle 3= m angle 2 + m angle 4

®  SPE (Subtraction)

×  m angle 1= m angle 2; m angle 3= m angle 4

×  m angle 1= m angle 3= m angle 2= m angle 4

®  MPE (Multiplication)

×  AB= CD; EF= GI

×  AB (EF)= CD (GI)

®  Substitution

×  A+ B= C; C=2

×  A+ B= 2