![]() We will review the ten postulates that we have learned so far, and add a few more problems dealing with perpendicular lines, planes, and perpendicular bisectors. Moreover, we will detail the process for coming up with reasons for our conclusions using known postulates. Whenever you see “con” that means you switch! It’s like being a con-artist! In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and contrapositive. ExampleĬontinuing with our initial condition, “If today is Wednesday, then yesterday was Tuesday.”īiconditional: “Today is Wednesday if and only if yesterday was Tuesday.” Are converse propositions universally true If not. In other words the conditional statement and converse are both true. When is one proposition said to be the converse or reciprocal of another Give examples. The contrapositive of a statement has its antecedent and consequent inverted and flipped. ExampleĬontrapositive: “If yesterday was not Tuesday, then today is not Wednesday” What is a Biconditional Statement?Ī statement written in “if and only if” form combines a reversible statement and its true converse. In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as proof by contraposition. Inverse: “If today is not Wednesday, then yesterday was not Tuesday.” What is a Contrapositive?Īnd the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both. Converse Statement: If a number is divisible by 2, then it is even. An example of a converse is: Original Statement: If a number is even, then it is divisible by 2. So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”. A simple example of a conditional statement is: If a function is differentiable, then it is continuous. Now the inverse of an If-Then statement is found by negating (making negative) both the hypothesis and conclusion of the conditional statement. So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.Ĭonverse: “If yesterday was Tuesday, then today is Wednesday.” What is the Inverse of a Statement? Hypothesis: “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.” ExampleĬonditional Statement: “If today is Wednesday, then yesterday was Tuesday.” ![]() Well, the converse is when we switch or interchange our hypothesis and conclusion. This is why we form the converse, inverse, and contrapositive of our conditional statements. Therefore, we sometimes use Venn Diagrams to visually represent our findings and aid us in creating conditional statements.īut to verify statements are correct, we take a deeper look at our if-then statements. Sometimes a picture helps form our hypothesis or conclusion. In fact, conditional statements are nothing more than “If-Then” statements! In this topic, we’ll figure out how to use the Pythagorean theorem and prove why it works. Even the ancients knew of this relationship. The Pythagorean theorem describes a special relationship between the sides of a right triangle. To better understand deductive reasoning, we must first learn about conditional statements.Ī conditional statement has two parts: hypothesis ( if) and conclusion ( then). Test your understanding of Pythagorean theorem with these (num)s questions. Here we go! What are Conditional Statements? In addition, this lesson will prepare you for deductive reasoning and two column proofs later on. ![]() We’re going to walk through several examples to ensure you know what you’re doing. It sets up some odd event, like parallel lines being crossed by a transversal, and then hopes you're astounded when that improbable event leads to something new, like alternate exterior angles.Įven when the lines are not parallel, alternate exterior angles exist, and we don't need to pull a rabbit out of a hat to amaze you with them.Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher) When is one proposition said to be the converse or reciprocal of another Give examples. Geometry is a bit like a magician's trick. You can now solve problems identifying and measuring alternate exterior angles. When lines crossed by the transversal are parallel, you can use the Alternate Exterior Angles Theorem to know the alternate exterior angles are congruent. If you are at the beach, then you are sun burnt. ![]() Now that you have gone through this lesson carefully, you are able to recall that angles on opposite sides of a transversal and outside two lines are called alternate exterior angles. If the converse is true, write the biconditional statement. The Alternate Exterior Angles Theorem tells us it is also 130°! Lesson summary That means ∠1 is its alternate exterior angle partner. ∠8 is on the outside of the bottom parallel line, and to the right of the transversal.
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