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Geometry Notes

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This lesson delves into the relationships between angles formed when two lines are intersected by a transversal. By exploring with and without technology, students will learn to classify various angle types such as vertical angles, linear pairs, corresponding angles, alternate interior angles, alternate exterior angles, and same-side interior angles. Engaging activities include labeling angles with colors and identifying sets of angles based on their relationships. This foundational knowledge is crucial for justifying when lines are parallel.

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Geometry Notes

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  1. Geometry Notes Lesson 2.1a Lines Cut By A Transversal LG.1.G.5 Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel

  2. Vocabulary • Transversal – A line that intersects two or more coplanar lines at different points  • Vertical Angles – non-adjacent, non-overlapping congruent angles formed by two intersecting lines . (They share a common vertex.) • Linear Pairs of Angles –two adjacent angles whose non-shared rays form a straight angle • Corresponding Angles – angles that lie on the same side of the transversal and in corresponding positions relative to the parallel lines

  3. Vocabulary • Alternate Interior Angles – nonadjacent angles between the parallel lines that lie on opposite sides of the transversal • Alternate Exterior Angles – nonadjacent angles outside the parallel lines that lie on opposite sides of the transversal • Same-Side Interior Angles – angles that lie on the same side of the transversal and between the parallel lines

  4. b a c Vertical Angles • Label by shading sets of vertical angles with the same color.

  5. b a c Linear Pairs of Angles • Label by shading linear pairs of angles with the same color.

  6. b a c Corresponding Angles • Label by shading sets of corresponding angles with the same color.

  7. b a c Alternate Interior Angles • Label by shading sets of alternate interior angles with the same color.

  8. b a c Alternate Exterior Angles • Label by shading sets of alternate exterior angles with the same color

  9. b a c Same-Side Interior Angles • Label by shading sets of same-side interior angles with the same color.

  10. Classifying Sets of Angles Given Two Transversals • Classify the given angles as either: alternate-interior angles; same-side interior angles; alternate exterior angles; corresponding angles; vertical angles; or none of these.

  11. 1 2 3 4 5 6 7 8 11 12 9 10 15 16 13 14 • 1 & 6 : ________ • 2 & 10 : _______ • 11 & 4 : _______ • 12 & 7 : _______ • 5 & 4 : _______ • 14 & 15: _______

  12. 6 2 1 3 4 5 8 9 10 11 7 12 13 14 • 2 & 7 : ______ • 3 & 5 : ______ • 7 & 14 : ______ • 8 & 2 : ______ • 13 & 7 : ______

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