When a conditional and its converse are true, you can combine them as a true ____. (1 point) counterexample biconditional unconditional hypothesis Show
Biconditional. When a conditional and its converse are true, you can combine them as a true biconditional. This is the statement you get by connecting the conditional and its converse with the word and. Expert answered|migzptz|Points 6813| Question Asked 10/8/2012 8:39:59 PM 0 Answers/Comments This answer has been confirmed as correct and helpful. Rating There are no new answers. Conditional & Converse StatementsGeometry is a wonderful part of mathematics for people who don't like a lot of numbers. It has shapes and angles, and it also has logic. Logic is formal, correct thinking, reasoning, and inference. Logic is not something humans are born with; we have to learn it, and geometry is a great way to learn to be logical.
Converse StatementsYou may know the word converse for a verb meaning to chat, or for a noun as a particular brand of footwear. Neither of those is how mathematicians use converse. Converse and inverse are connected concepts in making conditional statements. To create the converse of a conditional statement, switch the hypothesis and conclusion. To create the inverse of a conditional statement, turn both hypothesis and conclusion to the negative. Converse Statement Examples
Conditional StatementsConditional statements set up conditions that could be true or false. These conditions lead to a result that may or may not be true. Conditional statements start with a hypothesis and end with a conclusion. Conditional Statement Examples
You can always test the hypothesis. Does the polygon have four sides? Are the triangles congruent? If the hypothesis is false, the conclusion is false. Here are examples of conditional statements with false hypotheses:
You can test the hypothesis immediately: Are you 9 meters tall? Do squares have three sides? These conditional statements result in false conclusions because they started with false hypotheses. Creating Conditional StatementsConditional statements begin with "If" to introduce the hypothesis. The hypothesis is the part that sets up the condition leading to a conclusion. The conclusion begins with "then," like this:
You will see conditional statements in geometry all the time. You can set up your own conditional statements. Here is one for an isosceles triangle:
Exchanging Parts of Conditional StatementsYou can switch the hypothesis and conclusion of a conditional statement. You take the conclusion and make it the beginning, and take the hypothesis and make it the end:
Converse of a Conditional StatementThe converse of a true conditional statement does not automatically produce another true statement. It might create a true statement, or it could create nonsense:
That statement is true. But the converse of that is nonsense:
We know it is untrue because plenty of quadrilaterals exist that are not squares. Geometry and Conditional StatementsMany times in geometry we see postulates and theorems that seem like they could become conditional statements and converse conditional statements:
Example #2
Some postulates are even written as conditional statements:
Practice Conditional StatementsBelow we have equilateral triangle △NAP. We can set up conditional statements about it. Here are five statements. Decide which ones are conditional, which are not conditional, and which conditional statements are true:
Statements 1, 2, and 5 are all true conditional statements (If … then). Statement 3 is a converse of statement 2. Statement 4 is not a conditional statement, but it is true. You have enough information to change statement 4 into a conditional statement. Let's check the converse statement, 3, to see if it is true. Can you create a triangle with one interior angle measuring 60° but with the other angles having different measures? Of course you can, like a 30-60- 90 triangle, which is definitely not equilateral. So the converse statement is not true. Lesson SummaryIn this lesson you have learned to identify and explain conditional statements and create your own conditional statements. You know conditional statements could be true or false. You are able to exchange the hypothesis and conclusion of a conditional statement to produce a converse of the statement, and you can test to see if the converse of a true conditional statement is true. Next Lesson:Similarity Transformations What is it called when a conditional and its converse are true?Answer and Explanation: If a conditional and it's converse are always true, the statement is called a biconditional.
When a conditional and its converse are both true and combined the result is?A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form. Two line segments are congruent if and only if they are of equal length.
When the conditional and its converse are true the two statements can be combined to form a biconditional statement?A biconditional statement is a statement combing a conditional statement with its converse. So, one conditional is true if and only if the other is true as well. It often uses the words, "if and only if" or the shorthand "iff." It uses the double arrow to remind you that the conditional must be true in both directions.
Can the converse of a true statement be true?The truth value of the converse of a statement is not always the same as the original statement. For example, the converse of "All tigers are mammals" is "All mammals are tigers." This is certainly not true. The converse of a definition, however, must always be true.
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