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Perpendicular Lines, Parallel Lines and the Triangle Angle-Sum Theorem

Perpendicular Lines, Parallel Lines and the Triangle Angle-Sum Theorem. Parallel Lines. Parallel lines are coplanar lines that do not intersect. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||.

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Perpendicular Lines, Parallel Lines and the Triangle Angle-Sum Theorem

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  1. Perpendicular Lines, Parallel Lines and the Triangle Angle-Sum Theorem

  2. Parallel Lines • Parallel lines are coplanar lines that do not intersect. • Arrows are used to indicate lines are parallel. • The symbol used for parallel lines is ||. In the above figure, the arrows show that line AB is parallel to line CD. With symbols we denote, .

  3. Theorem 3-7 If a||b and b||c Then a||c a b c It 2 lines are parallel to the same line, then they are parallel to each other.

  4. m n PERPENDICULAR LINES • Perpendicular lines are lines that intersect to form a right angle. • The symbol used for perpendicular lines is  . • 4 right angles are formed. In this figure line m is perpendicular to line n. With symbols we denote, m n Lesson 2-3: Pairs of Lines

  5. Theorem 3-8 If and Then t m n In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.

  6. 3.3 Parallel Lines and the Triangle Angle-Sum Theorem • Theorem 3-10 Triangle Angle-Sum Theorem The angles in a triangle add up to 180°

  7. Triangle Angle-Sum Theorem Find m<1. 1 35° 65°

  8. Triangle Angle-Sum Theorem ΔMNP is a right triangle. <M is a right angle and m<N is 58°. Find m<P.

  9. Using Algebra G Find the values of x, y, and z. 39° 21° 65° x° y° z° F J H

  10. Classifying Triangles Equilateral: All sides congruent Equiangular: All angles congruent 60° 60° 60° Acute Triangle: All angles are less than 90° Right Triangle: One angle is 90° Obtuse Triangle: One angle is greater than 90°

  11. Classifying Triangles Isosceles: At least two sides congruent Scalene: No sides congruent

  12. Special Case Equiangular Triangle=Equilateral Triangle …and it’s also an Acute Triangle 60° 60° 60°

  13. Classifying a Triangle Classify the triangle by its sides and angles.

  14. Classifying a Triangle Classify the triangle by its sides and angles.

  15. Using Exterior Angles of Triangles Exterior Angle of a Polygon 1 Exterior Angle m<1 = m<2 + m<3 2 3 Remote Interior Angles Theorem 3-11 Triangle Exterior Angle Theorem The measure of the Exterior Angle is equal to the sum of the two Remote Interior Angles

  16. Using the Exterior Angle Theorem Find the missing angle measure: 113° 40° 1 30° 70° 2 45° 45° 3

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