Theorems
Terms
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- Same side Interior Angles Theorem
- If two lines cut by a transveral are parallel, then same-side interior angles are supplementary
- Converse of the Alternate Interior Angles Theorem
- If alternate interior angles are congruent then two lines cut by a transversal are parallel
- Corresponding Angles Postulate
- If two lines cut by a transversal are parallel, then the corresponding angles are congruent
- Transversal
- a line or ray that intersects to or more coplanar lines, rays, or segments, each at a different point.
- Corresponding Angles
- angles that are located in the same position in relation to a transversal
- Prove the Alternate Interior Angles Theorem
-
l and m are parallel lines given, m
- Theorem 2
- If two lines are parallel to the same line, then the two lines are parallel to each other
- Converse of the Same-side Interior Angles Theorem
- If the same-side interior angles are supplementary then the two lines cut by transversal are parallel
- Alternate Interior Angles Theorem
- If two lines cut a transversal are parallel then alternate interior angles are congruent
- Converse of Alternate Exterior Angles Theorem
- If alternate exterior angles are congruent, then two lines cut by a transversal are parallel
- Triangle Sum Theorem
- The sum of the measures of the angles of a triangle is 180 degrees
- The Parallel Postulate
- Given a line and a point not on that line, there is one and only one line the contains the given point and is parallel to the given line
- Alternate Exterior Angles Theorem
- If two lines cut by a transversal are parallel, then alternate exterior angles are congruent
- Theorem 1
- if 2 points are perpendicular to the same line, then the two lines are parallel to each other.
- Converse of the Corresponding Angles Postulate
- if corresponding angles are congruent then the two lines cut by a transversal are parallel