Question

Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."

Ruby writes, "Statement 3 is the inverse of statement 2 and contrapositive of statement 1."
Christine writes, "Statement 1 is the inverse of statement 2 and converse of statement 3."

Which option is true?

Both Ruby and Christine are correct.

Both Ruby and Christine are incorrect.

Only Ruby is correct.

Only Christine is correct.

Answer 1

@wio

Answer 2

what is the inverse of statement 2?

Answer 3

if A then B
Converse: if B then A
Inverse: if not A then not B
Contrapositive: if not B then not A

Answer 4

grrr so confused @wio

Answer 5

wait is it D?

Answer 6

If we say that statement 1 is "if A then B," then statement 2 would be the converse (if B then A), and statement 3 would be the contrapositive (If not B then not A).

Answer 7

First look at statement 2.

Identify A and B parts of it. The pattern is: if A then B

Answer 8

So let's take Ruby's response. Statement 3 is now "If A then B." The inverse would be "If not A then not B." and the contrapositive would be "If not B then not A." Statement 2 (if we say that statement 3 is "if A then B") is "If not A then B," which makes it the inverse. So the first part of Ruby's statement is correct.

Answer 9

So let's take Ruby's response. Statement 3 is now "If A then B." The inverse would be "If not A then not B." and the contrapositive would be "If not B then not A." Statement 2 (if we say that statement 3 is "if A then B") is ***"If not A then not B,"*** which makes it the inverse. So the first part of Ruby's statement is correct.

Answer 10

had to fix that...

Answer 11

You do the second part and Identify what kind of statement it is (e.g. contrapositive, inverse, converse, etc.)

Answer 12

Ok the inverse is "If she is stuck in traffic, then she is late" of statement two

Answer 13

Am I wrong?

Answer 14

Nope! :p

Answer 15

Can you help me with another question?

Answer 16

So that makes Ruby's statement correct. Now for Christine's. If Statement 2 is "If A then B," that makes Statement 1 "If B then A," which is the converse. So Christine's statement is wrong. The answer to the problem is "Only Ruby is correct," or C

Answer 17

Sure, @DEEISME, just post it the "Ask a question box"

Answer 18

If Johan completes his project, then he will visit the museum.

Which of these is logically equivalent to the given statement?

If Johan visits the museum, then he did not complete his project.

If Johan completes his project, then he will not visit the museum.

If Johan did not visit the museum, then he did not complete his project.

If Johan did not complete his project, then he will visit the museum.

Answer 19

What does logically equivalent mean?

Answer 20

It means you can use one of your logic statements (contrapositive, converse, etc) to find the answer. So if the statement "If Johan completes hos project, then he will visit the museum" is in the form "if A then B," which of the other statements is a contrapositive, converse, or inverse of the original statement?

Answer 21

Ohhh so it's C.

Answer 22

If he doesn't do it then he doesn't go.

Answer 23

Yup. The Inverse.

Answer 24

Anything else?

Answer 25

I have 3 more is that okay?

Answer 26

Sure!

Answer 27

Thanks

Answer 28

"If the alternate exterior angles are congruent, then the lines are parallel."

What is the inverse of the statement?

If the lines are parallel, then the alternate exterior angles are congruent.

If the alternate exterior angles are congruent, then the lines should be parallel.

If the alternate exterior angles are not congruent, then the lines are not parallel.

If the lines are not parallel, then the alternate exterior angles are not congruent.

Answer 29

I just get confused in the words.

Answer 30

if A then B
Converse: if B then A
Inverse: if not A then not B
Contrapositive: if not B then not A

Answer 31

Is it A.

Answer 32

So if the statement in the question is "If A then B," which of the other statements is in the form "If not A then not B?"

Answer 33

Oh I keep thinking it's the converse sorry it's D.

Answer 34

Nope! That would be the Contrapositive (If not B then not A)

Answer 35

Oh you keep it the statement the same it's C. I'm Sure I swear

Answer 36

Yassss you are!

Answer 37

YAY

Answer 38

Next?

Answer 39

Read the statement shown below:

"If the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle."

The converse of the statement is

If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle.

If the polygon is a triangle, then the sum of the interior angles of the polygon is not more than 180°.

If the sum of the interior angles of a polygon is equal to 180°, then the polygon is a triangle.

If the polygon is not a triangle, then the sum of the interior angles of the polygon is more than 180°.

Answer 40

Converse is "If B then A." Find it

Answer 41

D.

Answer 42

Yup.

Answer 43

Last one?

Answer 44

Read the statements shown below:

Statement 1: If it has two sides, then it is a polygon.
Statement 2: If it is not a polygon, then it does not have two sides.

Are the two statements logically equivalent?

No, both statements are false.

Yes, both statements are true.

No, only one statement is true.

Yes, both statements are false.

Answer 45

Ahhh I have another one after this I'm so sorry is that okay?

Answer 46

That's fine.

Answer 47

Thanks

Answer 48

Statement 2 is the contrapositive of statement 1. So it can be either B or D. But, think about your polygons to get the second part of the answer.

Answer 49

D.

Answer 50

Am I wrong @Nairz

Answer 51

nope.

Answer 52

sorry, had to pee.

Answer 53

In a geometry class, the students were asked to write statements that are logically equivalent to the statement shown below:

If a line segment joins the center of a circle with a point on the circle, then it is a radius.

Below are the responses of four students. Which student's response is correct?

Student 2: If a line segment is not a radius, then it joins the center of a circle with a point on the circle.

Student 1: If a line segment is not a radius, then it does not join the center of a circle with a point on the circle.

Student 3: If a line segment does not join the center of a circle with a point on the circle, then the line segment is a radius.

Student 4: If a line segment joins the center of a circle with a point on the circle, then the line segment is not a radius.

Answer 54

It's cool

Answer 55

I think it's B

Answer 56

So, which ones are "not - not" or "a - b"

Answer 57

Am I wrong... Umm B is a "Not - Not" the others are "Not - Are" or "Are - Not" @Nairz

Answer 58

B is right! That's the quickest way to throw-out answers that are not correct.

Answer 59

Any more? Willing to help with any geometry...

Answer 60

Umm sure not anymore like that though, is that okay?

Answer 61

Yeah, that's fine. If I know it, I will help.

Answer 62

Ok thanks


Perry observes the opposite, parallel walls of a room. In how many lines do the planes containing the walls intersect?

2

0

1

3

Answer 63

Okay, the key word in that question is PARALLEL.

Answer 64

Is it A?

Answer 65

No. What do parallel lines do?

Answer 66

They are lines that go in the same direction and don't intersect

Answer 67

Exactly. What do parallel planes do?

Answer 68

So C

Answer 69

No.

Answer 70

Oh wow it says intersect in the question so its 0

Answer 71

Parallel planes never intersect, just like parallel lines. So since the NEVER INTERSECT, how many lines do the PARALLEL planes intersect at?

Answer 72

Good job!

Answer 73

Martin drew a pair of perpendicular lines and a pair of parallel lines.

Which of these statements best compares the pairs of perpendicular and parallel lines?

Perpendicular and parallel lines have their lines extending in one direction only.

Perpendicular and parallel lines always have a common endpoint.

Perpendicular lines are lines that intersect at right angles, and parallel lines are lines that never meet.

Perpendicular lines have only one point lying on them, and parallel lines have no points lying on them.

Answer 74

Another one if you don't mind @Nairz

Answer 75

Sure

Answer 76

Okay, so which ones can you logically throw out?

Answer 77

The first one

Answer 78

And?

Answer 79

Well I get confused a lot but it says "and parallel lines are lines that never meet." I would say this is the right answer right?

Answer 80

Yes. Now, the second one is wrong because they gave us no endpoints for the lines in question. So, we are supposed to assume (in all of mathematics) that they are lines that go on forever; Therefore, B would be wrong. For the 4th one, lines are made up of infinitely many points, so D is wrong as well.

Answer 81

Next question?

Answer 82

Statement
Description

1 A line contains at least two points.
2 A plane contains at least three non-collinear points.


Which option best classifies Saul's statements?
Statement 1 is a theorem because it can be proved, and Statement 2 is a postulate because it is a true fact.

Statement 1 and Statement 2 are theorems because they can be proved.

Statement 1 and Statement 2 are postulates because they are true facts.

Statement 1 is a postulate because it is a true fact, and Statement 2 is a theorem because it can be proved.

Answer 83

umm.

Answer 84

Let me see if I remember...

Answer 85

I don't know what theorem or postulate are

Answer 86

Postulate means that it's definitely true. A theorem is something that can be proven as true, but isn't accepted as scientific or mathematical fact.

Answer 87

easier

Answer 88

So?

Answer 89

Which one is it?

Answer 90

A or B

Answer 91

I'm not sure, because A plane contains at least three non-collinear points thing

Answer 92

If I remember correctly, it's B. I'm not sure if those are postulates or theorems. I will leave that one

Answer 93

So, I don't know the answer, but those are questions to ask your teacher next time you talk to her.

Answer 94

or him.

Answer 95

I will.

Answer 96

The figure shows a partially completed set of steps to construct a rhombus PQRS:

Student 1 Fix the compass at M and adjust its width to point L. Without changing the width of the compass, move the compass to N and draw a small arc on the big arc. Label the point of intersection of the two arcs as T. Draw a line segment from P that passes through T. Adjust the width of the compass to QR and draw an arc from point P to intersect line PT at S.


Student 2 Fix the compass at M and draw an arc that intersects side QP at point T. Without changing the width of the compass, move the compass to R and draw an arc. Adjust the width of the compass to QR and draw an arc from point P. Draw a line segment from R that passes through T and intersects the second arc at S.


Student 3 Fix the compass at L and adjust its width to point M. Without changing the width of the compass, move the compass to R and draw an arc which intersects QR at point T. Draw a line segment from R that passes through T and intersects the arc at S.



Student 4 Fix the compass at L and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc which intersects QR at point T. Draw a line segment from R that passes through T and intersects the arc at S.


Which student used the correct steps to construct rhombus PQRS?
Student 2

Student 4

Student 3

Student 1

Answer 97

http://learn.flvs.net/webdav/assessment_images/educator_geometry/v15/module01/0100_g7_q2.jpg