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3.6: Prove Theorems about Perpendicular Lines Geometry 3.6: Prove Theorems about Perpendicular Lines
Theorems Theorem 3.8: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Theorem 3.9: If two lines are perpendicular, then they intersect to form 4 right angles. 1 2 1 2 3 4
Theorems Theorem 3.10: If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 1 2
Theorems Theorem 3.11: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Theorem 3.12: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
p.195 #15 and 17: Solve for x. 15.) 17.) 63 x+14 2x–9 x
Use the diagram below. r s t 1.) Is r s? 2.) Is m n? 3.) Is r t? m n
Homework Study Guide for Section 3.6
Chapter 3 Test (3.1-3.6) 3.1: Vocabulary 3.2: Parallel Lines Parallel, skew, perpendicular Alt. Int, Alt. Ext, Corresponding, Consec. Int. 3.2: Parallel Lines Alt. Int. angles, Alt. Ext. angles, and Corresponding angles are congruent. Consec. Int. angles are supplementary. 3.3: Determine if lines are parallel Converse of theorems
Chapter 3 Test (3.1-3.6) 3.4: Slope- Determine if lines are parallel, perpendicular, or neither. Parallel lines: same slope Perpendicular lines: slopes are negative reciprocals 3.5: Lines Graphing Write equation of lines using either: y = mx + b y – y1 = m(x – x1) Write equations of lines parallel or perp. to other lines given graph or equation.
Chapter 3 Test (3.1-3.6) 3.6: Perpendicular Lines Theorems Identify if lines are parallel given information. Solve for x