Geometry Homework Practice Workbook 1st Edition Chapter 2 Inductive Reasoning and Conjecture
Page 19 Problem 1 Answer
We are given a conditional statement ‘If you purchase a computer and do not like it, then you can return it within 30 days’.
We are required to identify the hypothesis and the conclusion.
Since, the given statement is in the ”if-then” form, we can say that the statement after ‘if’ will be the hypothesis and the statement after ‘then’ will be the conclusion.
That is, we have the hypothesis-you purchase a computer and do not like it and the conclusion-you can return it within 30 days.
In the given conditional statement, If you purchase a computer and do not like it, then you can return it within 30 days, we have the hypothesis-you purchase a computer and do not like it and the conclusion-you can return it within 30 days.
Page 19 Problem 2 Answer
We are given a conditional statement ‘If x+8=4, then x=−4’.We are required to identify the hypothesis and the conclusion.
Since, the given statement is in the ”if-then” form, we can say that the statement after ‘if’ will be the hypothesis and the statement after ‘then’ will be the conclusion.
That is, we have, hypothesis-x+8=4 and the conclusion-x=−4
For the given conditional statement ‘If x+8=4,then x=−4’, we have,the hypothes is -x+8=4 and the conclusion-x=−4
Page 19 Problem 3 Answer
We are given a conditional statement ‘If the drama class raises $2000, then they will go on tour’.We are required to identify the hypothesis and the conclusion.
Since, the given statement is in the ”if-then” form, we can say that the statement after ‘if’ will be the hypothesis and the statement after ‘then’ will be the conclusion.
That is, we have,the hypothesis- the drama class raises $2000 and the conclusion- they will go on tour
For the given conditional statement, ‘If the drama class raises $2000, then they will go on tour’, we have the hypothesis – the drama class raises $2000 and the conclusion – they will go on tour.
Page 19 Problem 4 Answer
We are given a statement ‘A polygon with four sides is a quadrilateral’.We are required to write it in the if-then form.
Here, we can write it as,If a polygon has four sides, then it is a quadrilateral.
The given statement ‘A polygon with four sides is a quadrilateral’ can be written in the if-then form as ‘If a polygon has four sides, then it is a quadrilateral’.
Page 19 Problem 5 Answer
We are given a statement ‘An acute angle has a measure less than 90’.We are required to write this in the if-then form.
We can formulate it as, If an angle measures less than 90, then it is an acute angle.
The statement ‘An acute angle has a measure less than 90’, can be written in the if-then form as, ‘If an angle measures less than 90, then it is an acute angle’.
Page 19 Problem 6 Answer
We are given a conditional statement ‘If you have five dollars, then you have five one-dollar bills’.We are required to it’s truth value.
The given conditional statement is False. As the conditional hypothesis is correct, but the conclusion is incorrect.
As a counter example, we know that five-dollars equals one five-dollar bill only.
Hence, we cannot have five-one dollar bills when you have five dollars.
The given a conditional statement ‘If you have five dollars, then you have five one-dollar bills’ if false.
As a counter example, we know that five-dollars equals one five-dollar bill only.
Hence, we cannot have five-one dollar bills when you have five dollars.
Page 19 Problem 7 Answer
In this question, a given statement is “If I roll two six-sided dice and the sum of the numbers is 11, then one die must be a five”.
Here, we have to tell the truth value of the given conditional statement.
We have to tell If the given statement is true then we have to explain reasoning but if the statement is false then we have to give a counterexample.
When this hypothesis is true, the conclusion is also true.
The sum can only be 11 if one die is a6 and the other is a 5.
The conditional statement is true.
Hence, the given conditional statement “If I roll two six-sided dice and the sum of the numbers is 11, then one die must be a five.” is true.
Page 19 Problem 8 Answer
In this question, a given statement is “If two angles are supplementary, then one of the angles is acute.”Here, we have to tell the truth value of the given conditional statement.
We have to tell If the given statement is true then we have to explain reasoning but if the statement is false then we have to give a counterexample.
False; both angles could be right angles. The hypothesis of the conditional is true, but the conclusion is false.
This counterexample shows that the conditional is false.
Hence, the given conditional statement “If two angles are supplementary, then one of the angles is acute.” is false.
Page 19 Problem 9 Answer
In this question, a given statement is “If 89 is divisible by 2, then 89 is an even number.”
Here, we have to write converse, inverse, and contra positive of the given conditional statement.
We have to tell If the given statement is true or false but if the statement is false then we have to give a counterexample.
So, Converse Statement is If 89 is an even number, then 89 is divisible by 2. which is true.
Inverse Statement is If 89 is not divisible by 2, then 89 is not an even number; which is true.
Contra positive Statement is If 89 is not an even number, then 89 is not divisible by 2. which is true.
Hence, the given statement “If 89 is divisible by 2, then 89 is an even number” is true for converse, inverse, and contra positive statements.
Page 20 Problem 10 Answer
Here, the given conditional statement is “If 3x+4=−5, then x=−3”.
As we know, The hypothesis of a conditional statement is the phrase immediately following the word if.
And The conclusion of a conditional statement is the phrase immediately following the word then.
So, the hypothesis is “3x+4=−5”.And the conclusion is “x=−3”
Hence, from the given statement “If3x+4=−5, then x=−3”
The hypothesis is “3x+4=−5” and the conclusion is “x=−3”.
Page 20 Problem 11 Answer
Here, the given conditional statement is “If you take a class in television broadcasting, then you will film a sporting event”.
As we know, The hypothesis of a conditional statement is the phrase immediately following the word if.
And The conclusion of a conditional statement is the phrase immediately following the word then.
So, the hypothesis is “you take a class in television broadcasting”.
And the conclusion is “you will film a sporting event”
Hence, from the given statement “If you take a class in television broadcasting, then you will film a sporting event” the hypothesis is “you take a class in television broadcasting” and the conclusion is “you will film a sporting event”.
Page 20 Problem 12 Answer
In this question, the given statement is “Those who do not remember the past are condemned to repeat it.”
We have to write the given statement in if-then form.
So, To write these statements in if-then form, identify the hypothesis and conclusion.
The word if is not part of the hypothesis.
The word then is not part of the conclusion.
So, the statement is “If you do not remember the past, then you are condemned to repeat it.”
Hence, the statement in if-then form is “If you do not remember the past, then you are condemned to repeat it”.
Page 20 Problem 13 Answer
In this question, the given statement is ” Adjacent angles share a common vertex and a common side.”
We have to write the given statement in if-then form.
So, To write these statements in if-then form, identify the hypothesis and conclusion.
The word if is not part of the hypothesis. The word then is not part of the conclusion.
So, the statement is “If two angles are adjacent, then they share a common vertex and a common side.”
Hence, the statement in if-then form is “If two angles are adjacent, then they share a common vertex and a common side.”
Page 20 Problem 14 Answer
In this question, a given statement is “If a and b are negative, then a+b is also negative.”
Here, we have to tell the truth value of the given conditional statement.
We have to tell If the given statement is true then we have to explain reasoning but if the statement is false then we have to give a counterexample.
When this hypothesis is true, the conclusion is also true.
A negative added to another negative will just go further negative.
The conditional statement is true.
Hence, the given conditional statement “If a and b are negative, then a+b is also negative” is true.
Page 20 Problem 15 Answer
In this question, a given statement is “If two triangles have equivalent angle measures, then they are congruent.”Here, we have to tell the truth value of the given conditional statement.
We have to tell If the given statement is true then we have to explain reasoning but if the statement is false then we have to give a counterexample.
False, two triangles could have the same angle measures but different side lengths.
The hypothesis of the conditional is true, but the conclusion is false.
This counterexample shows that the conditional is false.
Hence, the given conditional statement “If two triangles have equivalent angle measures, then they are congruent” is false.
Page 20 Problem 16 Answer
In this question, a given statement is ” If the moon has purple spots, then it is June.”Here, we have to tell the truth value of the given conditional statement.
We have to tell If the given statement is true then we have to explain reasoning but if the statement is false then we have to give a counterexample.
When this hypothesis is false, the statement is true.
So, the given statement is true.
Hence, the given conditional statement “If the moon has purple spots, then it is June” is true.
Page 20 Problem 17 Answer
We are given, that older campers who attend Woodland Falls Camp are expected to work. Campers who are juniors wait on tables.
We have to write a conditional statement in if-then form.
The conditional statement will be: If you are an old camper who attends Woodland Falls Camp then you are expected to work and if you are junior camper then you have to wait on table.
The conditional statement in if-then form for the given statement will be: If you are an old camper who attends Woodland Falls Camp then you are expected to work and if you are junior camper then you have to wait on table.
Page 20 Problem 18 Answer
We are given, that older campers who attend Woodland Falls Camp are expected to work.
Campers who are juniors wait on tables. We have to write the converse of your conditional statement.
The conditional statement was: If you are an old camper who attends Woodland Falls Camp then you are expected to work and if you are junior camper then you have to wait on table.
Its converse statement will be: If you are expected to work then you are an old camper who attends Woodland Falls Camp and if you have to wait on table then you are junior camper.
Its converse statement for the conditional statement will be: If you are expected to work then you are an old camper who attends Woodland Falls Camp and if you have to wait on table then you are junior camper.