![]() ![]() Similarly, a and d are also alternate interior angles.Ĭo-interior angles are the two interior angles that are on the same side of the transversal which makes it supplementary and sums up to 180 degrees. Here, p and q are alternate interior angles. ![]() Make a zig-zag line including the parallel lines as shown in the diagram. In the case of non – parallel lines, alternate interior angles don’t have any specific properties.įor finding alternate interior angles, we use the Z test.The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°.If we have two lines (they don't have to be parallel) and have a third line that crosses them, then the crossing line is said to be a transversal.Two lines that never intersect, are equidistant, and are coplanar are called parallel lines.Here are a few properties of the alternate interior angles: Remember the lines do not have to be always parallel for alternate angles to be formed.Īlternate interior angles are: ∠3 and ∠6, ∠4 and ∠5Īlternate exterior angles are: ∠1 and ∠8, ∠2 and ∠7 Properties of Alternate Interior Angles Alternate exterior angles: Alternate exterior angles are formed on the exterior of the coplanar lines but on the alternate opposite sides of the transversal.Īlternate interior angles are: ∠3 and ∠6, ∠4 and ∠5.Īlternate exterior angles are: ∠1 and ∠8, ∠2 and ∠7.įor example: Let us try to spot alternate interior angles in the given figure.They are on the inner side of the coplanar lines but are on the alternate opposite sides of the transversal. Alternate interior angles: Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.Alternate angles are of two types: Alternate interior angles and Alternate exterior angles When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. Corresponding angles in the above image are: ∠2 and ∠4, ∠1 and ∠3, ∠5 and ∠7, and ∠6 and ∠8. Corresponding angles formed by two parallel lines and a transversal are equal. Co-interior angles are supplementary when the lines are parallel.Ĭorresponding angles are a pair of angles on the similar corners of each of two lines on the same side of the transversal line. Interior angles on the same side of the transversal are called consecutive interior angles or co-interior angles in short. Since the given lines m and n are parallel, therefore the alternate interior angles will be congruent. In the figure given below, a set of parallel lines m and n are intersected by the transversal and the following pairs of alternate interior angles are formed: ∠1 and ∠2, ∠3 and ∠4. The alternate interior angles theorem states that if a transversal crosses the set of parallel lines, the alternate interior angles are congruent. ![]() When we previously discussed inductive reasoning we based our reasoning on examples and on data from earlier events.What is the Alternate Interior Angles Theorem? If we instead use facts, rules and definitions then it's called deductive reasoning. We will explain this by using an example. If you get good grades then you will get into a good college. The part after the "if": you get good grades - is called a hypotheses and the part after the "then" - you will get into a good college - is called a conclusion. Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.Ī conditional statement is false if hypothesis is true and the conclusion is false. The example above would be false if it said "if you get good grades then you will not get into a good college". If we re-arrange a conditional statement or change parts of it then we have what is called a related conditional. Our conditional statement is: if a population consists of 50% men then 50% of the population must be women. If we exchange the position of the hypothesis and the conclusion we get a converse statement: if a population consists of 50% women then 50% of the population must be men. A conditional and its converse do not mean the same thing If both statements are true or if both statements are false then the converse is true. If we negate both the hypothesis and the conclusion we get a inverse statement: if a population do not consist of 50% men then the population do not consist of 50% women. The inverse is not true juest because the conditional is true. The inverse always has the same truth value as the converse. We could also negate a converse statement, this is called a contrapositive statement: if a population do not consist of 50% women then the population do not consist of 50% men. The contrapositive does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true.Ī pattern of reaoning is a true assumption if it always lead to a true conclusion.
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