Question

Nathan, Joshua, Michelle, and Denise were in a room where a porcelain vase was found broken. When an inquiry was conducted by the building caretaker, each made a statement.

Nathan: Joshua broke the vase.
Joshua: Nathan did not do it.
Michelle: Joshua lied when he said Nathan did not do it.
Denise: Joshua did it.

The caretaker knew that only one statement is not true and concluded that Michelle broke the vase.

Describe in complete sentences the method you use to show that the caretaker made an incorrect conclusion.

Answer 1

This is my answer...is it correct?
Assume that Michelle did not break the vase. Based on the assumption, Nathan's statement that Joshua broke the vase is TRUE. Based on the assumption, Joshua's statement that Nathan did not do it is TRUE. Based on the assumption, Michelle's statement that Joshua lied when he said Nathan did not do it is FALSE. Finally, based on the assumption, Denise's statement that Joshua did it is TRUE. Since one of the four statements contradicts the assumption, the assumption is false. This means that Michelle did not break the vase.

Answer 2

You did great!
*like a boss*

Answer 3

I agree :)

Answer 4

Can you check this one as well?
Jazz draws a transversal, t, on two parallel lines AB and CD, as shown below.



He makes the following table to prove that the alternate interior angles are equal.

Answer 5

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0908_11/image0014e734293.jpg

Answer 6

Statement
Justification
angle 2 = angle 6
Corresponding angles of parallel lines are congruent.
angle 2 = angle 4
?
angle 4 = angle 6
transitive property of equality,
angle 2 = angle 6,
angle 2 = angle 4,
therefore angle 4 = angle 6

Answer 7

Which is the missing justification?

Angles 1 and 3 are supplementary; therefore, angle 2 is equal to angle 4.

Angles 1 and 3 are congruent; therefore, angle 2 is equal to angle 4.

Angles 1 and 4 and angles 1 and 2 are supplementary; therefore, angle 2 is equal to angle 4.

Angles 1 and 4 and angles 1 and 2 are congruent; therefore, angle 2 is equal to angle 4.

Answer 8

i think it's the third one

Answer 9

That would be correct.

Answer 10

Btw, if you ever do a proof yourself in a situation like this, don't say that reason, but rather vertical angles. Just a tip there...