GEOMETRY 3.4 Perpendicular Lines

LEARNING TARGETS  Students should be able to…  Prove and apply theorems about perpendicular lines.

WARM-UP 1. Name the line that is the transversal. 2. Name the parallel lines. 3. Name all the pairs of Corresponding Angles. 4. Name all the pairs of Alternate Interior Angles. 5. Name all the pairs of Alternate Exterior Angles. 6. Name all pairs of Consecutive Interior Angles. 7. Name all pairs of Consecutive Exterior Angles. 8. Name all pairs of Vertical Angles.

GO OVER QUIZ

VOCABULARY TermNameDiagramAdditional Notes Perpendicular Bisector A line perpendicular to a segment at the segments midpoint AB l M

VOCABULARY TermNameDiagramAdditional Notes Perpendicular Bisector A line perpendicular to a segment at the segments midpoint Distance from a point to a line AB l M AC B P

CONSTRUCTION OF A PERPENDICULAR BISECTOR OF A SEGMENT A B C D

SECTION 3-4 POSTULATES & THEOREMS  POSTULATE: Parallel Postulate: If a point is not on a line, then there is 1 line that can be drawn through it so that it is parallel to the first line.

SECTION 3-4 POSTULATES & THEOREMS  POSTULATE - Perpendicular Postulate: If a point is not on a line, then there is 1 line that can be drawn through it so that it is perpendicular to the first line.

SECTION 3-4 POSTULATES & THEOREMS  Theorem: If 2 lines are parallel to the same line, they are parallel to each other.

SECTION 3-4 POSTULATES & THEOREMS  Theorem 3-4-1: If 2 intersecting lines form a linear pair of congruent angles, then the lines are perpendicular.

SECTION 3-4 POSTULATES & THEOREMS  Theorem 3-4-2: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

SECTION 3-4 POSTULATES & THEOREMS  Theorem 3-4-3: If 2 lines are perpendicular to the same line, then they are parallel to each other.

PRACTICE PROBLEMS

4 8 90º

PRACTICE PROBLEMS

5

x +5 < 9, x < 9

PRACTICE PROBLEMS x + 5 > 9, x > 11

PRACTICE PROBLEMS

D

HOMEWORK  Page 174 – 175 #2, 3, 6, 7, 10 – 15