11/12/14 Geometry Bellwork 1.3x = 8x – 15 0 = 5x – = 5x x = 3 2.6x + 3 = 8x – 14 3 = 2x – = 2x x = x – 2 = 3x + 6 2x – 2 = 6 2x = 8 x = 4 AB = 2 AM AB = 2(5x – 2) AB = 2(5*4 – 2) = 2(18) AB = 36

5.2: Use Perpendicular Bisectors Objective: Use perpendicular bisectors to solve problems A line segment (or line or ray) is a perpendicular bisector if it is perpendicular to another segment at its midpoint

Geometry – Standard G.PL.3 Prove and apply theorems about lines and angles, including the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and corresponding angles are congruent; when a transversal crosses parallel lines, same side interior angles are supplementary; and points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the segment. POINTS, LINES, ANGLES

Geometry – Standard G.PL.5 Explain and justify the process used to construct, with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.), congruent segments and angles, angle bisectors, perpendicular bisectors, altitudes, medians, and parallel and perpendicular lines. POINTS, LINES, ANGLES

equidistant CB

AB 4x7x x 4(2) 8

Check Points #1 and 2

Concurrency Concurrent – Three or more lines, rays, or segments that intersect in the same point Point of concurrency – The point of intersection of the lines, rays, or segments

Work these out now! 2x = 5x – 6 0 = 3x – 6 6 = 3x x = 2 AB = 4 3x + 8 = 7x – 16 8 = 4x – = 4x x = 6 AB = 26 6x + 11 = 11x – 9 11 = 5x – 9 20 = 5x x = 4 AB = 35

Homework 11/12/14 Pages: : Exercises: 3-5 all, even, 24, 37, 38