31.Identify the Hypothesis of the statement below.
If you are riding on a train, then it will stop at every station on the line.
A.You are riding on a train
B.It will stop at every station on the line
C.You are not riding on a train
D.It will not stop at every station on the line.
32.Identify the conclusion of the statement below.
If a football player scores a touchdown, then the player’s team earns 6 points.
A.A football player scores a touchdown
B.The players team earns 6 points
C.A football player does not score a touchdown
D.The players team does not earn 6 points
Use the statement below to answer questions 33-35
If a triangle has three congruent sides, then it has three congruent angles.
33.What is the converse of the statement above?
A.If a triangle does not have three congruent sides, then it does not have three congruent angles.
B.If a triangle has three congruent angles, then it has three congruent sides.
C.If a triangle does not have three congruent angles, then it does not have three congruent sides.
D.If a triangle has three congruent sides, then it has three congruent angles.
34.What is the inverse of the statement above?
A.If a triangle does not have three congruent sides, then it does not have three congruent angles.
B.If a triangle has three congruent angles, then it has three congruent sides.
C.If a triangle does not have three congruent angles, then it does not have three congruent sides.
D.If a triangle has three congruent sides, then it has three congruent angles.
35.What is the contrapositive of the statement above?
A.If a triangle does not have three congruent sides, then it does not have three congruent angles.
B.If a triangle has three congruent angles, then it has three congruent sides.
C.If a triangle does not have three congruent angles, then it does not have three congruent sides.
D.If a triangle has three congruent sides, then it has three congruent angles.
For the statement below write the converse of the statement and determine if the converse is true or false.
36.If a shape is a rectangle then it is a parallelogram.
A.If a shape is not a rectangle, then it is not a parallelogram TRUE
B.If a shape is not a rectangle, then it is not a parallelogram, FALSE
C.If a shape is a parallelogram, then it is a rectangle, TRUE
D.If a shape is a parallelogram then it is a rectangle, FALSE
For the statement below write the contrapositive and determine if the contrapositive is true or false.
37.If a shape is a rectangle then it has 4 right angles.
A.If a shape is not a rectangle, then it does not have 4 right angles. TRUE
B.If a shape is not a rectangle, then it does not have 4 right angles, FALSE
C.If a shape does not have 4 right angles, then it is not a rectangle, TRUE
D.If a shape does not have 4 right angles, then it is not a rectangle, FALSE
Determine if each statement below is valid. If it is valid did you verify it using the Law of Syllogism or the Law of Detachment.
38.If the measure of two angles have a sum of 180 degrees then the angles are supplementary. M<A+m<B= 180 degrees. <A and <B are supplementary.
A.Valid, Law of Syllogism
B.Valid, Law of Detachment
C.Valid, but it doesn’t use either law
D.Invalid
39.If a triangle has two congruent sides, then the triangle is an isosceles triangle. In triangle NYU NY=UN. Therefore Triangle NYU is an Isosceles triangle.
A.Valid, Law of Syllogism
B.Valid, Law of Detachment
C.Valid, but it doesn’t use either law
D.Invalid
40.If you live in Providence, then you live in Rhode Island. If you live in Rhode Island, then you live in the smallest state in the USA. Karen lives in Providence. Therefore Karen lives in the smallest state in the USA.
A.Valid, Law of Syllogism
B.Valid, Law of Detachment
C.Valid, but it doesn’t use either law
D.Invalid
31. The hypothesis of the statement is: A. You are riding on a train.
To identify the hypothesis of a conditional statement, look for the part that comes after the "if" and before the "then". In this case, it is the statement "You are riding on a train."
32. The conclusion of the statement is: B. The player's team earns 6 points.
To identify the conclusion of a conditional statement, look for the part that comes after the "then". In this case, it is the statement "The player's team earns 6 points."
33. The converse of the statement is: B. If a triangle has three congruent angles, then it has three congruent sides.
To find the converse of a conditional statement, switch the hypothesis and the conclusion. In this case, the original statement is "If a triangle has three congruent sides, then it has three congruent angles." So, the converse is "If a triangle has three congruent angles, then it has three congruent sides."
34. The inverse of the statement is: C. If a triangle does not have three congruent sides, then it does not have three congruent angles.
To find the inverse of a conditional statement, negate both the hypothesis and the conclusion. In this case, the original statement is "If a triangle has three congruent sides, then it has three congruent angles." So, the inverse is "If a triangle does not have three congruent sides, then it does not have three congruent angles."
35. The contrapositive of the statement is: A. If a triangle does not have three congruent sides, then it does not have three congruent angles.
To find the contrapositive of a conditional statement, negate both the hypothesis and the conclusion, and then switch them. In this case, the original statement is "If a triangle has three congruent sides, then it has three congruent angles." So, the contrapositive is "If a triangle does not have three congruent sides, then it does not have three congruent angles."
36. The converse of the statement is: C. If a shape is a parallelogram, then it is a rectangle.
To find the converse of a conditional statement, switch the hypothesis and the conclusion. In this case, the original statement is "If a shape is a rectangle, then it is a parallelogram." So, the converse is "If a shape is a parallelogram, then it is a rectangle."
In this case, the converse is true because a parallelogram can have other shapes besides rectangles.
37. The contrapositive of the statement is: C. If a shape does not have 4 right angles, then it is not a rectangle.
To find the contrapositive of a conditional statement, negate both the hypothesis and the conclusion, and then switch them. In this case, the original statement is "If a shape is a rectangle, then it has 4 right angles." So, the contrapositive is "If a shape does not have 4 right angles, then it is not a rectangle."
In this case, the contrapositive is true because shapes that do not have 4 right angles are not rectangles.
38. The statement is valid and uses the Law of Detachment.
The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion must be true. In this case, the statement is "If the measure of two angles have a sum of 180 degrees, then the angles are supplementary." The given information is "M<A+m<B= 180 degrees" which satisfies the hypothesis of the statement. Therefore, we can conclude that "<A and <B are supplementary" using the Law of Detachment.
39. The statement is valid and uses the Law of Syllogism.
The Law of Syllogism states that if two conditional statements are true and the conclusion of the first statement is the hypothesis of the second statement, then the conclusion of the second statement is true. In this case, the first statement is "If a triangle has two congruent sides, then the triangle is an isosceles triangle." The second statement is "Triangle NYU has two congruent sides" which satisfies the conclusion of the first statement. Therefore, we can conclude that "Triangle NYU is an isosceles triangle" using the Law of Syllogism.
40. The statement is valid and uses the Law of Syllogism.
The Law of Syllogism states that if two conditional statements are true and the conclusion of the first statement is the hypothesis of the second statement, then the conclusion of the second statement is true. In this case, the first statement is "If you live in Providence, then you live in Rhode Island." The second statement is "Karen lives in Providence" which satisfies the conclusion of the first statement. Therefore, we can conclude that "Karen lives in the smallest state in the USA" using the Law of Syllogism.