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Common Core Standards Parallel Lines cut by a Transversal
CCSS.MATH.CONTENT.HSG.CO.C.11
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
CCSS.MATH.CONTENT.HSG.CO.D.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
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Fun Class Activities Incorporating Parallel Lines and Transversals
Parallel Lines Cut by a Transversal Guided Notes
Parallel lines are coplanar lines that do not intersect. The symbol ∥ means “is parallel to.”
When a line intersects two or more lines, the angles formed at the intersection points create special angle pairs.
A transversal is a line that intersects two or more coplanar lines at distinct points.
The special angle pairs formed by parallel lines and a transversal are congruent, supplementary, or both.
Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate interior angles are congruent.
Corresponding Angles Theorem
If a transversal intersects two parallel lines, then corresponding angles are congruent.
Same-Side Interior Angles Postulate
If a transversal intersects two parallel lines, then same-side interior angles supplementary.
Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then alternate exterior angles are congruent.
Sample Problem 1:
Identify all the angles that are congruent to the given angle.
Sample Problem 2:
Identify all the angles that are supplementary to the given angle.
Sample Problem 3:
Find the value of x.
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