Lines and Angles

Question 1

Postulate or Axiom

Answer 1

Rules that are accepted without proof

Question 2

Ruler Postulate

Answer 2

The points on a line can be matched one-to-one with the real numbers - real numbers that correspond to a point are called coordinantes.

Question 3

Segment Addition Postulate

Answer 3

if we have a line segment AC and a point B within it, the sum of the lengths of the segments AB and BC will give the total length of AC.

Question 4

Protractor Postulate

Answer 4

The rays in a half rotation can be numbered from 0 to 180. The
measure of ÐAOB is equal to the absolute value of the difference between
the real numbers for lines OA and OB.

Question 5

Angle Addition Postulate

Answer 5

If P is in the interior of angle RST then the measure of angle RSP + the measure of angle PST = measure of angle RST.

Line divides one triangle into two triangles each side adds up to each other

Question 6

Distance Formula

Answer 6

Distance = SQRT(x2 - x1)^2 + (y2 - y1)^2

Question 7

Acute Angle Definition

Answer 7

An angle is acute IFF it is less than 90 degrees

Question 8

Right Angle Definition

Answer 8

An angle is right IFF it is 90 degrees

Question 9

Obtuse Angle Definition

Answer 9

An angle is obtuse IFF it is more than 90 degrees and less than 180

Question 10

Straight Angle Definition

Answer 10

An angle is straight IFF it is 180 degrees

Question 11

Adjacent Angles Definition

Answer 11

Two angles are said to be adjacent IFF they share a common vertex and side but have no common interior points.

Question 12

Congruent Angles “Definition” no IFF

Answer 12

Angles that have the same measure are called congruent – angles are congruent IFF they have the same measure.

Question 13

Midpoint Definition

Answer 13

A point is a midpoint of a line segment IFF it divides the line segment into two equal segments. (each side of the midpoint is equal)

Question 14

Bisect Definition

Answer 14

A line bisects an angle IFF it divides the angle into two adjacent angles that are congruent (two equal angles)

Trisecting splits an angle into three equal parts

Question 15

Addition Property of Equality

Answer 15

x-7 = 4
+7. +7.

x = 11

Question 16

Subtraction Property of Equality

Answer 16

If a=b then a-c = b-c

Question 17

Multiplication Property of Equality

Answer 17

If a=b then ac = bc, c=/0

Question 18

Division Property of Equality

Answer 18

if a=b then a/c = b/c c/=0

Question 19

Substitution Property of Equality

Answer 19

If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression

Question 20

Reflexive Property

Answer 20

a=a ab=ab mangle A = mangle A

Question 21

Symmetric Property

Answer 21

if a=b then b=a and so one for angles and lines

Question 22

Transitive Property

Answer 22

if a=b and b=c then a=c
if ab=bc and bc=cd then ab=cd
if m/a = m/b and m/b = m/c m/a=m/c

Question 23

Complementary Angles Definition

Answer 23

Two angles are complementary IFF their sum is 180 degrees. Each angle is the complement of the other.

Question 24

Supplementary Angles Definition

Answer 24

Two angles are supplementary IFF their sum is 180 degrees. Each angle is a supplement of the other.

Question 25

Opposite Rays Definition

Answer 25

Two rays are called opposite rays IFF their rays point in opposite directions.

Question 26

Linear Pair Definition

Answer 26

Two adjacent angles are a linear pair IFF their noncommon sides are opposite rays.

Question 27

Vertical Angles Definition

Answer 27

Two angles are vertical angles IFF their sides form two pairs of opposite rays.