Chapter 6

Question 1

properties of inequality

Answer 1

If a > b and c > or = d, then a + c > b + d.

If a > b and c > 0, then ac > bc and a/c > b/c.

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

If a = b + c and c > 0, then a > b.

Question 2

exterior angle inequality theorem

Answer 2

the measure of an exterior angle of a triangle is greater than the measure of either remote interior angle

Question 3

inverse

Answer 3

the negative version of a conditional statement

Question 4

contrapositive

Answer 4

the negative version of a converse

Question 5

logically equivalent

Answer 5

a conditional and a contrapositive will be both true or false, the converse and inverse will both be true or false

Question 6

indirect proof

Answer 6

1. assume temporarily that the conclusion is not true
2. reason logically until you reach a contradiction of the know fact (given)
3. point out that the temporary assumption is false, and that the conclusion must then be true

Question 7

theorem 6-2

Answer 7

if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side

Question 8

theorem 6-3

Answer 8

if one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle

Question 9

corollary 1

Answer 9

the perpendicular segment from a point to a line is the shortest segment from the point to the line

Question 10

corollary 2

Answer 10

the perpendicular segment from a point to a plane is the shortest segment from the point to the plane

Question 11

the triangle inequality theorem

Answer 11

the sum of the lengths of any two sides of a triangle is greater than the length of the third side