Chapter 2 - Deductive Reasoning and Perpendicular Lines

Question 1

converse of if p, then q

Answer 1

if q, then p

Question 2

biconditional of if q, then p

Answer 2

p if and only if q

Question 3

addition property of equality

Answer 3

if a = b, c = d, then a + c = b + d

Question 4

subtraction property of equality

Answer 4

if a = b, c =d, then a - c = b - d

Question 5

multiplication property of equality

Answer 5

if a = b, then ca = cb

Question 6

division property of equality

Answer 6

if a = b and c != 0, then a/c = b/c

Question 7

substitution property of equality

Answer 7

if a = b then either a or b may be substituted for the other in any equation or inequality

Question 8

reflexive property of equality

Answer 8

a = a

Question 9

symmetric property of equality

Answer 9

if a = b then b = a

Question 10

transitive property of equality

Answer 10

if a = b and b = c then a = c

Question 11

what are the properties of congruence?

Answer 11

reflexive, symmetric, transitive

Question 12

midpoint theorem

Answer 12

if M is the midpoint of AB, then AM = ½AB and MB = ½AB

Question 13

angle bisector theorem

Answer 13

if BX is the bisector of angle ABC, them m ABX = ½mABC and mXBC = ½mABC

Question 14

complementary angles

Answer 14

sum 90

Question 15

supplementary angles

Answer 15

sum 180

Question 16

if two lines are perpendicular

Answer 16

if two lines are perpendicular, they form congruent adjacent angles

Question 17

if two lines form congruent adjacent angles

Answer 17

if two lines form congruent adjacent angles, the lines are perpendicular

Question 18

if the exterior sides of two adjacent acute angles are perpendicular…

Answer 18

if the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary

Question 19

if two angles are supplements or complements of congruent angles (or the same angle)

Answer 19

then the two angles are congruent

Question 20

definition of perpendicular lines

Answer 20

two lines that intersect at a 90° angle