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Mastering Geometry Theorems: Proving Perpendicular Lines

Explore theorems 3.8 to 3.12 in geometry, proving perpendicular lines and related concepts. Solve for x in practical exercises and enhance understanding of parallel and perpendicular lines. Perfect for Chapter 3 test preparation.

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Mastering Geometry Theorems: Proving Perpendicular Lines

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  1. Do Now

  2. Geometry 3.6: Prove Theorems about Perpendicular Lines

  3. 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

  4. Theorems • Theorem 3.10: If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 1 2

  5. 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.

  6. p.195 #15 and 17: Solve for x. 15.) 17.) 63 x+14 2x–9 x

  7. Use the diagram below. r s t 1.) Is r s? 2.) Is m n? 3.) Is r t? m n

  8. Homework • Study Guide for Section 3.6

  9. Chapter 3 Test (3.1-3.6) • 3.1: Vocabulary • 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

  10. 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.

  11. Chapter 3 Test (3.1-3.6) • 3.6: Perpendicular Lines Theorems • Identify if lines are parallel given information. • Solve for x

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