Angles Formed by Parallel Lines and Transversals 1 The Corresponding Angles Postulate states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent 2 Congruent angles have equal measures Find each angle measure 140° 1 70° 2 3 m 1 140 4 m 2 70 Findx 5 90° ( 15)° 6 120° ( 30)°
Warm-Up Exercises 3 1 Identify Pairs of Lines and Angles 3 2 Use Parallel Lines and Transversals 3 3 Prove Lines are Parallel 3 4 Find and Use Slopes of Lines 3 5 Write and Graph Equations of Lines 3 6 Prove Theorems About Perpendicular Lines CHAPTER 3: Parallel and Perpendicular Lines
The two parallel lines LM and NP are intersected by the line RS The arrows pointing to the same direction indicate that the lines are parallel (i) The corresponding angles are equal a = e b = f c = g d = h (ii) The alternate angles are equal c = e d = f (iii) The sum of two allied angles is 180o c + f = 180o d + e = 180o
In Exercises 5–10, give one example of each from the figure 5 a transversal 6 parallel lines 7 corresponding angles _____ _____ _____ 8 alternate interior angles 9 alternate exterior angles 10 same-side interior angles _____ _____ _____ Use the figure for Exercises 11–14 The figure shows a utility pole with an electrical line and a
Lines that intersect at right angles are called perpendicular lines Indicates lines and m are perpendicular m p q Indicates lines and are parallel q p A line that intersects two or more lines is called a transversal When parallel lines are cut by a transversal, several pairs of congruent angles are formed Exercises 7–9 b t a 110° 2 1
Mathematics Grade 8 5 REMEMBER: Adjacent angles on a straight line are supplementary If they are adjacent angles on a straight line, then they add up to 180°
Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal, the following pairs of angles are congruent • corresponding angles • alternate interior angles • alternate exterior angles Also, consecutive interior angles are supplementary In the figure, m∠2 = 75 Find the measures of the remaining angles
find unknown values in angles formed by a transversal and parallel lines Example If ml-I = 3x + 15, ml-2 = 4x — 5, 111/—3 = 5y, and nzL4 = 6z + 3, find x and y p Il q, so m Ll = m L 2 because they are corresponding angles r Il s, so mL2 = m because they are corresponding angles 3x + 15 = 3x + 15 — 3x 15 +5 20 Exercises x 5 5-3x mL2 15 =
3 1 Measuring Angles A protractor can be used to measure or draw angles Note The angle around a complete circle is is 360o The angle around a point on a straight line is 180o Worked Example 1 Measure the angle CAB in the triangle shown Solution Place a protractor on the triangle as shown The angle is measured as 47o Worked Example 2
Jamais 9 1 III Refaites-vous les exercices qui y sont traités à titre d'exemples? "Elève Pythagore, sortez de cet angle ou je vous mets la tête au carré'' 1'élève dont il corrige la copie n'a pas suivi le même enseignement parallél ou du triang 28 22 1 lisme, la propriété tenant lieu d'associativité étant celle qui est
AAP