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 It 2 lines are parallel to the same line, then they are parallel to each other.

Lesson 2-3: Pairs of Lines4 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. m n In this figure line m is perpendicular to line n. With symbols we denote, m  n

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

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°

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

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

Using Algebra Find the values of x, y, and z. FJH G 39° 65°x°x° 21° y°y°z°z°

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

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

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

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

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

Using Exterior Angles of Triangles Exterior Angle of a Polygon 1 Exterior Angle 23 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 m<1 = m<2 + m<3

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