unit 6: inequalities

Question 1

kite

Answer 1

a quadrilateral that has exactly 2 pairs of consecutive congruent sides

Question 2

kite diagonals theorem

Answer 2

if a quadrilateral is a kite, then its diagonals are perpendicular

Question 3

kite opposite angles theorem

Answer 3

if a quadrilateral is a kite, then exactly 1 pair of opposite angles are congruent

Question 4

properties of inequality

Answer 4

1. if a > b & c > d, then a+b > c+d
2. if a > b & c > 0, then ac > bc & a/c > b/c
3. if a > b & c < 0, then ac < bc & a/c < b/c
4. if a > b & b > c, then a > c
5. if a = b+c & c > 0, then a > b

Question 5

exterior angle inequality theorem

Answer 5

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

Question 5

conditional statement

Answer 5

“if p, then q”

Question 5

converse

Answer 5

“if q, then p” (reversed)

Question 6

inverse

Answer 6

“if not p, then not q” (negated)

Question 7

biconditional

Answer 7

“p if and only if q”

Question 8

contrapositive

Answer 8

“if not q, then not p” (both reversed and negated)

Question 9

what is important about contrapositives?

Answer 9

if a conditional is true, then the contrapositive is always true too
note: converses & inverses are NOT always true

Question 10

how to write an indirect proof?

Answer 10

prove the contrapositive true!
1. make assumption that the conclusion is untrue
2. reason until contradiction is reached
3. explain contradiction and therefore conclusion true

Question 11

what must an indirect proof always have?

Answer 11

an assumption, contradiction, and conclusion

Question 12

triangle longer side theorem

Answer 12

if 1 side of a triangle is longer than a 2nd side, then the angle opposite the 1st side is larger than the angle opposite the 2nd side

Question 13

triangle larger angle theorem

Answer 13

if 1 angle of a triangle is larger than a 2nd angle, then the side opposite the 1st angle is longer than the side opposite the 2nd angle

Question 14

triangle larger angle corollaries

Answer 14

1. the perpendicular segment from a point to a line is the shortest segment from the point to the line
2. the perpendicular segment from a point to a plane is the shortest segment from the point to the plane

Question 15

triangle inequality theorem

Answer 15

the sum of 2 side lengths of a triangle is always greater than the length of the 3rd side