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Understanding Angle Relationships and Parallel Lines in Geometry

Learn about types of angles including acute, obtuse, and right angles, as well as complementary and supplementary angles. Explore adjacent, congruent, and corresponding angles along with the properties of intersecting lines. Practice identifying and calculating angle measurements.

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Understanding Angle Relationships and Parallel Lines in Geometry

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  1. Lesson 9.2 Angle Relationships and Parallel Lines .

  2. Types of Angles Acute - Obtuse - Angles that measure less than 90. Angles that measure more than 90 and less than 180. Right - Angles that measure exactly 90.

  3. Adjacent Angles • Share a vertex and a side but no points in the interiors. <AXB and <BXC are adjacent angles B A <AXC and <BXC are not adjacent angles Why? X C

  4. Complementary Angles - Angles whose sum is 90 . a b Complementary angles do not have to be adjacent. x y

  5. Supplementary Angles - Angles whose sum is 180 . k t Supplementary angles do not have to be adjacent. b c

  6. Congruent Angles • Angles that have the same measurement • Notation:

  7. Vertical Angles - Opposite angles that are formed by intersecting lines. a Opposite angles (vertical angles) are ALWAYScongruent. b

  8. Identifying Corresponding Angles Transversal -A line that intersects two other lines.

  9. Identifying Corresponding Angles Corresponding Angles - Two angles that are formed by two lines and a transversal and occupy corresponding positions. A B 1 2 3 4 5 6 7 8 C D Corresponding Angles If the two lines are parallel, then the corresponding angles are congruent.

  10. Identifying Alternate Interior Angles Alternate Interior Angles: -interior of a pair of lines on opposite sides of the transversal. A B 1 2 3 4 5 6 7 8 C D Corresponding Angles If the two lines are parallel, then the alternate interior angles are congruent.

  11. Find the value of n. 1) 2)

  12. Homework • Page 452 -453 (1-11 all and 13) • Draw figures in the homework

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