When you have two parallel lines cut by a … Working Scholars® Bringing Tuition-Free College to the Community. When the lines that the transversal intersects are parallel, you get same-side interior angles that are supplementary, or add up to 180 degrees. Favorite Answer. Same-Side Interior Angles Converse Theorem If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are _____, then the two lines are parallel. Same Side Interior Angles Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines. The same rule applies to the smallest sized angle and side, and the middle sized angle and side. Get the unbiased info you need to find the right school. Lines a and b are parallel to each other! If you don't know if the lines in a diagram are parallel, but you know that the same-side interior angles add up to 180 degrees, it's safe to draw the conclusion that the lines cut by the transversal line are parallel and vice versa. You can sum up the above definitions and theorems with the following simple, concise idea. When transversal line t intersects parallel lines a and b, it makes the same-side interior angles 3 and 6 supplementary. Write the converse of the Alternate Exterior Angles Theorem. ... Angles on the same side of a transversal and inside the lines it intersects. Prove that if alternate interior angles are congruent, then the lines that form them are parallel. credit-by-exam regardless of age or education level. So we know that 52 + y = 180. and career path that can help you find the school that's right for you. 1 Answers. Same-side interior angles: Angles 3 and 5 (and 4 and 6) ... Same-side exterior angles: Angles 1 and 7 (and 2 and 8) are called same-side exterior angles — they’re on the same side of the transversal, and they’re outside the parallel lines. To better organize out content, we have unpublished this concept. Then we know that s = 128 since z + s = 180 since they form the transversal line. 3) The lines, A and B, in the image below are NOT parallel. Same-side interior angles add up to 180 degrees. 4) The lines, A and B, in the image below are parallel. Not sure what college you want to attend yet? Rule 4 Remote Extior Angles -- This Theorem states that the measure of a an exterior angle $$ \angle A$$ equals the sum of the remote interior angles' measurements. Anyone can earn 's' : ''}}. Triangle Sum Theorem The sum of the interior angles of a triangle equals 180 degrees. Angles formed on the same side of the transversal involving two parallel lines are supplementary. Same-Side Interior Angles Theorem The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where :According to the given information, is parallel to , while angles SQU and VQT are vertical angles. 2) Since the lines A and B are parallel, the same-side interior angles theorem states that same-side interior angles will be supplementary. Converse of the Same Side Interior Angles Theorem: If two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel. 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). If the interior alternating angles … In the applet below, a TRANSVERSAL intersects 2 PARALLEL LINES. Referring to the figure above, the transversal AB crosses the two lines PQ and RS, creating intersections at E and F. Each pair of interior … Answer Save. Same Side Interior Angles Theorem. There are n angles in a regular polygon with n sides/vertices. How do we know this? Therefore, we know that the same-side interior angles 3 and 6 are supplementary, or that they add up to 180 degrees. example of same side exterior angles same side exterior angles theorem. She has over 10 years of teaching experience at high school and university level. Visit the High School Geometry: Tutoring Solution page to learn more. 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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). Assume L||M and the above angle assignments. The postulate for the alternate interior angles states that: If a transversal intersects … 2) The lines, A and B, in the image below are parallel. Converse of Same Side Interior Angles Theorem. Earn Transferable Credit & Get your Degree, Same-Side Exterior Angles: Definition & Theorem, Alternate Exterior Angles: Definition & Theorem, Corresponding Angles: Definition, Theorem & Examples, Alternate Interior Angles: Definition, Theorem & Examples, The Perpendicular Transversal Theorem & Its Converse, Remote Interior Angles: Definition & Examples, The Parallel Postulate: Definition & Examples, Linear Pair: Definition, Theorem & Example, Angle Addition Postulate: Definition & Examples, What is a Paragraph Proof? 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