![]() ![]() Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100) Learn more. It tracks your skill level as you tackle progressively more difficult questions. ![]() The next three examples use these results in coordinate geometry. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. Let's do that here, too: m∠1 + m∠4 = 180° as a linear pair, m∠5 + m∠4 = 180° is given, so m∠5=m∠1, and by the converse of the corresponding angles theorem, the lines are parallel. O Figure 5.28 The converse of each of the three circle properties above is also true. In proving the original theorem, we relied on the fact that a linear pair of angles are supplementary. So it makes sense to start by looking at what we did in the original theorem. A converse of a theorem is a statement formed by interchanging what is given in a theorem and what is to be proved. What is a converse example A converse of an if-then statement is created by swapping the IF and the THEN parts. M∠5 + m∠4 = 180°, prove that AB||CD Strategy The example above would be false if it said 'if you get good grades then you will not get into a good college'. A conditional statement is false if hypothesis is true and the conclusion is false. We will show that if the consecutive interior angles on the same side of a transversal line intersecting two lines are supplementary, then the two lines are parallel. Hypotheses followed by a conclusion is called an If-then statement or a conditional statement. Here we will prove its converse of that theorem. The Consecutive Interior Angles Theorem states that the consecutive interior angles on the same side of a transversal line intersecting two parallel lines are supplementary (That is, their sum adds up to 180). In today's lesson, we will show a simple method for proving the Consecutive Interior Angles Converse Theorem. For example, the converse of 'If it is raining then the grass is wet' is 'If the grass is wet then it is raining. ![]()
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