unit 6 because idk shit

Question 1

Properties of inequalities 1

Answer 1

If a > b, and c ≥ d, then a + c > b + d (LIKE ADD. PROP.)

Question 2

Properties of inequalities 1 EX

Answer 2

a = 5
b = 2
c = 3
d = 1

5 >2
+3 +1

8 > 3

Stays true

Question 3

Properties of inequalities 2

Answer 3

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

Question 4

Properties of inequalities 2 EX

Answer 4

  2

OR FOR NEGATIVES,

 -2

Remember, sign FLIPS when dividing or multiplying negative numbers

Question 5

Properties of inequalities 3

Answer 5

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

Question 6

Properties of inequalities 4

Answer 6

If a > b and b > c, then a > c (LIKE TRANS. PROP.)

Question 7

Properties of Inequalities 5

Answer 7

If a = b + c and c > 0, then a > b (SUM IS GREATER THAN ITS PARTS”

Question 8

PRACTICE: If XY = YZ + 5, then XY > YZ (T or F)

Answer 8

True

Question 9

PRACTICE: If m<A = m<B +m<C, then m<b> m<C (T or F)</b>

Answer 9

False

Question 10

PRACTICE: If m<H = m<J + m<K, then m<K> m<H</K>

Answer 10

False

Question 11

PRACTICE: If 10 = y + 2, then y > 10

Answer 11

False

Question 12

The Exterior Angle Inequality Theorem

Answer 12

The measure of exterior angles of a triangle is greater than the measures of either remote interior angle.

Question 13

-Statement: If p, then q.
-What is the Inverse?

Answer 13

If not p, then not q

Question 14

-Statement: If p, then q.
-What is the Contrapositive?

Answer 14

If not q, then not p

Question 15

If the statement is true (or false),

Answer 15

Then the contrapositive is true (or false)

Question 16

Statements and contrapositives of those statements are called what?

Answer 16

Logically equivalent statements

Question 17

What does a conditional venn diagram look like?

Answer 17

Circle p is inside circle q

Question 18

PRACTICE: (If p, then q.) All runners are athletes. Leroy is a runner. What’s the conclusion?

Answer 18

Leroy is an athlete.

Question 19

PRACTICE: (If p, then q.) All runners are athletes. Lucia is not an athlete. What’s the conclusion?

Answer 19

Lucia is not a runner.

Question 20

PRACTICE: (If p, then q.) All runners are athletes. Linda is an athlete. What’s the conclusion

Answer 20

No conclusion.

Question 21

PRACTICE: (If p, then q.) All runners are athletes. Larry is not a runner. What’s the conclusion?

Answer 21

No conclusion.

Question 22

What do indirect proofs start with?

Answer 22

“Assume that (opp. of what your proving is true)”

Question 23

How to write an Indirect proof?

Answer 23

1. Assume temporarily that the conclusion is not true
2. Reason logically until you reach a contradiction of a known fact
3. Point out that the temporary assumption is false and the conclusion is true.

Question 24

PRACTICE:
Given: n is an integer and n^2 is even
Prove: n is even

Answer 24

SOMETHING LIKE THIS:
-Assume temporarily that n is not even
-Then n is odd and
n^2 = n x n
=odd x odd
=odd
This however contradicts the original given information that n^2 is even, meaning the assumption was false and that n is even

Question 25

If one side of a triangle is longer than the second side,

Answer 25

Then the angle opposite to the first side is larger than the angle opposite the second side

Question 26

If one angle of a triangle is larger than a second angle,

Answer 26

Then the side opposite to the first angle is longer than the side opposite to the second angle.

Question 27

The perpendicular segment from a point to a line is-

Answer 27

-the shortest segment from the point to the plane.

Question 28

The perpendicular segment from a point to a plane is-

Answer 28

-the shortest segment from the point to the plane.

Question 29

The sum of the lengths of any two sides of a triangle is-

Answer 29

-greater than the lengths of the third side.

Question 30

Is it possible for a triangle to have sides with the following lengths?

6, 8, 10

Answer 30

Yes

Question 31

Is it possible for a triangle to have sides with the following lengths?

3, 4, 8

Answer 31

No

Question 32

Is it possible for a triangle to have sides with the following lengths?

2.5, 4.1, 5.0

Answer 32

Yes

Question 33

Is it possible for a triangle to have sides with the following lengths?

6, 6, 5

Answer 33

Yes queen

Question 34

SAS Inequality Theorem

Answer 34

If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Question 35

SSS Inequality Theorem

Answer 35

If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.