Parallel Lines and Perpendicularity

ACTIVITY NO.5: PICTURE ANALYSIS Parallel lines cut by a transversal have various application to real life. In fact, you can see these lines all over the world. Now, look around you and cite example that illustrate parallel lines cut by a transversal. Example1: The Pasig City LGU made a wheel chair ramp for PWDs. If the Railings of a wheelchair ramp is parallel in each other. Find the value of x that will make m II n D Solution 1: MLA = (4x + 4)0 MLB = 760 mLC = (5x + 14)0 mLD = 1040 MLA = MLB Since LA and LB are alternate Interior angles, then they are congruent. Solve for the value of x (4x + 4)0 = 760 Substitution 4x = 76 - 4 Addition Property of Equality (APE) 4x = 72 Combine like terms X = 18 Solution 2: mLC = mLD Since LC and LD are corresponding angles, then they are congruent. Solve for the value of x (5x + 14)0 = 1040 Substitution 5x = 104 - 14 Addition Property of Equality (APE) 5x = 90 Combine like term X = 18Perpendicular 90 perpendicular distance between the parallel lines Perpendicular bisector (XY = YZ) perpendicular to the line segment and intersects it at its midpoint. The distance between two parallel lines is the perpendicular distance between one of the lines. The small rectangle drawn on intersecting lines indicates a "right angle". The 1 symbol indicates perpendicularity of lines as XZ 1 PY. To prove that two lines are perpendicular, you must show that one of the following theorems is true, 1. If two lines are perpendicular to each other, then they form four right angles. Ifwin, then 21, 22 63, and 24 are right angles. 2. If the angles in a linear pair are congruent, then the lines containing their sides are perpendicular. If