Converse of corresponding angles postulate

What is the Converse of the Corresponding Angles Postulate? Nov 5, Theorem Converse of the. Same-Side Interior Angles Postulate. Theorem. If. Then. If two lines and a transversal form same-side.

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In order to study geometry in a logical way, it will be important to understand key mathematical properties and to know how to apply useful postulates and theorems. A postulate is a proposition that has not been proven true, but is considered to be true on the basis for mathematical reasoning. Theorems , on the other hand, are statements that have been proven to be true with the use of other theorems or statements. While some postulates and theorems have been introduced in the previous sections, others are new to our study of geometry. We will apply these properties, postulates, and theorems to help drive our mathematical proofs in a very logical, reason-based way. Before we begin, we must introduce the concept of congruency. Angles are congruent if their measures, in degrees, are equal.

This lesson investigates and use the alternate interior angles theorem, the alternate exterior angles theorem, the corresponding angles postulate, the same side interior angles theorem and the same side exterior angles theorems. The other post titled, Geometry — Properties of Parallel Lines , would not allow me to put up my other video, so here is the 1st video lesson on properties of parallel lines. This lesson investigates and use the converse of alternate interior angles theorem, the converse of alternate exterior angles theorem, the converse of corresponding angles postulate, the converse of same side interior angles theorem and the converse of same side exterior angles theorem. The first problem in the video covers determining which pair of lines would be parallel with the given information. You are given that two same-side exterior angles are supplementary. There two pairs of lines that appear to parallel.

Consider two statements: A Two lines that are cut by a transversal are parallel B Alternate interior angle formed by these lines are congruent They are equivalent. See below for explanation. Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. Let's represent it in a form "if A then B": If two lines that are cut by a transversal are parallel [Part A] then alternate interior angles formed by these lines are congruent [Part B]. Converse theorem should look like "if B then A": If alternate interior angles formed by these lines are congruent [Part B] then two lines that are cut by a transversal are parallel [Part A]. So, these are two different theorems, each requiring its own proof. If one is true, another is as well, if one if false, another is well.

A transversal is a straight line that crosses two or more straight lines. In this lesson, we will focus on transversals that cross two or more parallel lines. When a line called a transversal intersects a pair of parallel lines, corresponding angles are formed. Corresponding angles are angles that are in the same relative position at an intersection of a transversal and at least two lines. If the two lines are parallel then the corresponding angles are congruent. One way to find the corresponding angles is to draw a letter F on the diagram.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math Geometry all content Angles Angles between intersecting lines. Missing angles with a transversal. Practice: Angle relationships with parallel lines. Missing angles CA geometry.

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Corresponding Angles Postulate

. Proof of Corresponding Angles Converse

Parallel lines & corresponding angles proof

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1. Generoso O. says:
2. Finley S. says: