We can set up conditional statements about it. If two points lie in a plane, then the line joining them lies in that plane.īelow we have equilateral triangle △NAP. If two parallel lines are cut by a transversal, then the corresponding angles are congruent. Some postulates are even written as conditional statements: If angles are adjacent, then they share a common side. If angles share a common side, then they are adjacent. (Converse)Īdjacent angles share a common side. If two lines never meet, then they are parallel. If two lines are parallel, then they are lines that never meet. Many times in geometry we see postulates and theorems that seem like they could become conditional statements and converse conditional statements: We know it is untrue because plenty of quadrilaterals exist that are not squares. If a polygon is a quadrilateral, then it is also a square. If a polygon is a square, then it is also a quadrilateral. It might create a true statement, or it could create nonsense: The converse of a true conditional statement does not automatically produce another true statement. If triangles have equal corresponding sides, then they are congruent. If my dog observes something that excites him, then he barks. You take the conclusion and make it the beginning, and take the hypothesis and make it the end: You can switch the hypothesis and conclusion of a conditional statement. If the triangle is isosceles, then only two of its sides are equal in length.Įxchanging parts of conditional statements You can set up your own conditional statements. You will see conditional statements in geometry all the time. If my dog barks, then my dog observed something that excited him. The conclusion begins with "then," like this: Creating Conditional Statements (If, Then) The hypothesis is the part that sets up the condition leading to a conclusion. Creating conditional statementsĬonditional statements begin with "If" to introduce the hypothesis. These conditional statements result in false conclusions because they started with false hypotheses. You can test the hypothesis immediately: Are you 9 meters tall? Do squares have three sides? If a square has three sides, then its interior angles add to 180°. If I am 9 meters tall, then I can play basketball. Here are examples of conditional statements with false hypotheses: Does the polygon have four sides? Are the triangles congruent? If the hypothesis is false, the conclusion is false. If triangles are congruent, then they have equal corresponding angles. If a polygon has exactly four sides, then it is a quadrilateral. If my cat is hungry, then she will rub my leg. Conditional statements start with a hypothesis and end with a conclusion. These conditions lead to a result that may or may not be true. ( Inverse)Ĭonverse Statement Examples Conditional statementsĬonditional statements set up conditions that could be true or false. If I do not eat a pint of ice cream, then I will not gain weight. If I gained weight, then I ate a pint of ice cream. If I eat a pint of ice cream, then I will gain weight. Converse and Inverse of a Conditional Statement Converse statement examples To create the inverse of a conditional statement, turn both hypothesis and conclusion to the negative. To create the converse of a conditional statement, switch the hypothesis and conclusion. Converse and inverse are connected concepts in making conditional statements. Neither of those is how mathematicians use converse. You may know the word converse for a verb meaning to chat, or for a noun as a particular brand of footwear.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |