Does Exterior Angle Theorem Imply Parallel Lines?

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When two lines are parallel, the transversal creates congruent alternate exterior angles. The theorem says: The Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

does exterior angle theorem imply parallel lines?


⏯ – Corresponding Angles Theorem with Parallel Lines


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⏯ – Proof: Corresponding angle equivalence implies parallel lines


⚡Popular questions on the topic: “does exterior angle theorem imply parallel lines?”⚡

Are exterior angles of parallel lines equal?

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent. The picture above shows two parallel lines with a transversal.
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Do consecutive exterior angles prove parallel lines?

Consecutive Exterior Angle Converse Theorem If two lines are cut by a transversal and the consecutive exterior angles are supplementary, then the two lines are parallel.
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What theorem proves angles are parallel?

Comparing postulate 10 to postulate 11, what do you notice? If two parallel lines are cut by a transversal, then corresponding angles are congruent. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
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What does the exterior angle theorem tell us?

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.
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How do you find the exterior angle of a parallel line?

1:213:03Using Alternative Exterior Angles to Find the Value of X – YouTubeYouTube
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Which situation tells about parallel lines?

To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.
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What is the rule for parallel lines?

The rule for parallel lines is that the lines should not meet each other. In other words, if two straight lines in the same plane are the same distance apart and they never meet each other, they are called parallel lines.
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How do you show that two lines are parallel?

To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.
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Which theorem can be used to prove two lines are parallel?

Theorem 10.8: If two lines are cut by a transversal so that the alternate interior angles are congruent, then these lines are parallel. Theorem 10.9: If two lines are cut by a transversal so that alternate exterior angles are congruent, then these lines are parallel….Geometry.

StatementsReasons
6.l mTheorem 10.7

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How do you determine if two lines are parallel?

0:193:59How To Tell If Two Lines Are Parallel, Perpendicular, or Neither? – YouTubeYouTube
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Which of the following theorems reveals that the measure of an exterior?

The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
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Which relationship is supported by the exterior angle theorem?

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles. Remember that the two non-adjacent interior angles opposite the exterior angle are sometimes referred to as remote interior angles.
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What is the equation for parallel lines?

In a linear equation of the form y=mx+b, parallel lines will always have the same m.
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What statement is true about parallel lines?

Solution: Two or more lines that lie in the same plane and never intersect or meet each other are known as parallel lines. (a) Parallel lines never intersect with each other or meet at any point. So, this statement is true.
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Which statement must be true for the two lines to be parallel?

Two lines are parallel if and only if they have the same slope. The slope of one of the lines is . The slope of the other is, so the lines have the same slope. The lines are parallel.
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How do you prove two lines are parallel?

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. Proof Ex.
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Which of the following is true about parallel lines?

Solution: Two or more lines that lie in the same plane and never intersect or meet each other are known as parallel lines. (a) Parallel lines never intersect with each other or meet at any point. So, this statement is true.
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What are the theorems to prove two lines parallel?

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
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How do you prove two lines are parallel without angles?

If two lines have a transversal which forms alternative interior angles that are congruent, then the two lines are parallel. If two lines have a transversal which forms corresponding angles that are congruent, then the two lines are parallel.
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How do you find the parallel lines theorem?

If interior angles on the same side of the transversal sum to 180, then lines are parallel. If Alternate Interior angles have equal measure, then lines are parallel.
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⏯ – Geometry – What are the Angle Theorems for Parallel Lines and a Transversal


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