Rules for Angle and Segment Proofs

Question 1

What is the addition property of equality?

Answer 1

If a = b, then a+b = b+c.

Question 2

What is the subtraction property of equality?

Answer 2

If a=b, then a-c = b-c.

Question 3

What is the multiplication property of equality?

Answer 3

If a = b, then ac = bc.

Question 4

What is the division property of equality?

Answer 4

If a = b, then a/c = b/c.

Question 5

What is the distributive property?

Answer 5

If a(b+c), then a(b+c) = ab + ac.

Question 6

What is the substitution property?

Answer 6

If a = b, then “a” may be replaced by “b” in any expression or equation.

Question 7

What is the reflexive property?

Answer 7

For any real number a = a.

Question 8

What is the symmetric property?

Answer 8

If a = b, then b = a.

Question 9

What is the transitive property?

Answer 9

If a = b, and b = c, then a = c.

Question 10

What is the reflexive property of congruence?

Answer 10

For any segment AB, AB is congruent to AB.

Question 11

What is the symmetric property of congruence?

Answer 11

If segment AB is congruent to segment CD, then segment CD is congruent to segment AB.

Question 12

What is the transitive property of congruence?

Answer 12

If segment AB is congruent to segment CD, and segment CD is congruent to segment EF, then segment AB is congruent to segment EF.

Question 13

What is the definition of congruence?

Segments

Answer 13

Segments are congruent if and only if they have the same measure:

If segment AB is congruent to segment CD, the AB = CD.
If AB = CD, then segment AB is congruent to segment CD.

Question 14

What is the definition of a midpoint?

Answer 14

The midpoint of a segment divides the segment into two equal (congruent) parts:

If M is the midpoint of AB, then AM = MB.

Question 15

What is the segment addition postulate?

Answer 15

If A, B, and C are collinear points and B is between A and C:

then segment AB + segment BC = segment AC.

Question 16

What is the definition of congruence?

angles

Answer 16

The measure of angle A = the measure of angle B is the same as angle A is congruent to angle B.

Question 17

What is the definition of an angles bisector?

Answer 17

An angle bisector divides an angle into two equal parts.

Question 18

What is the definition of complementary angles?

Answer 18

Sum is 90 degrees or it is complementary.

Question 19

What is the definition of supplementary angles?

Answer 19

Sum is 180 degrees or it is supplementary.

Question 20

What is the definition of perpendicular?

Answer 20

Perpendicular lines form right angles.

Question 21

What is the definition of a right angle?

Answer 21

A right angle = 90 degrees.

Question 22

What is the definition of angle addition postulates?

Answer 22

The measure of angle ABC + the measure of angle DBC = angle ABC.

Question 23

What is the vertical angles theorem?

Answer 23

If two angles are vertical, then they are congruent.

Question 24

What is the complement theorem?

Answer 24

If two angles form a right angle, then they are complementary:

Right Angle implies Complementary.

Question 25

What is the supplement theorem?

Answer 25

If two angles form a linear pair, then they are supplementary:

Linear Pair implies Supplementary.

Question 26

What is the congruent complements theorem?

Answer 26

If angle A is complementary to angle B, and angle B is complementary to angle C, then angle A is congruent with angle C.

Question 27

What is the congruent supplements theorem?

Answer 27

If angle A is supplementary to angle B, and angle B is supplementary to angle C, then angle A is congruent with angle C.