Pearson Unit 1 Topic 3: Parallel and Perpendicular Lines 3-4: Parallel and Perpendicular Lines Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (6)(A) Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angle formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems. (1)(G) Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication. (1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace.

Example: 1 Write a two-column proof. Given: r || s, 1  2 Prove: r  t Statements Reasons 1. r || s, 1  2 1. Given 2. 2  3 2. Corr. s Post. 3. 1  3 3. Transitive Prop. of  4. 2 intersecting lines form lin. pair of  s  lines . 4. r  t

Example: 2 Write a two-column proof. Given: Prove: Statements Reasons 1. EHF  HFG 1. Given 2. 2. Conv. of Alt. Int. s Thm. 3. 3. Given 4. 4.  Transv. Thm.

Example: 3 A carpenter’s square forms a right angle. A carpenter places the square so that one side is parallel to an edge of a board, and then draws a line along the other side of the square. Then he slides the square to the right and draws a second line. Why must the two lines be parallel? Both lines are perpendicular to the edge of the board. Theorem: If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

Example: 4 A swimmer who gets caught in a rip current should swim in a direction perpendicular to the current. Why should the path of the swimmer be parallel to the shoreline? Path of the swimmer is  to the current. Shoreline is  to the current. Therefore, shoreline and path of swimmer are || to each other.

Example: 5 A carpenter is building a trellis for vines to grow on. The completed trellis will have 2 sets of diagonal pieces of wood that overlap each other. A. If pieces A, B, and C must be parallel, what must be true of 1, 2, and 3? Justify the answer. 1, 2, and 3 are congruent by the Corresponding Angles Postulate. B. The carpenter attaches piece D so that it is perpendicular to piece A. Is piece D also perpendicular to pieces B and C? Justify your answer. D is perpendicular to B and C by the Perpendicular Transversal Theorem.

Example: 6 The map is a section of a subway map. brown pink Yel low bl ue G r e n The map is a section of a subway map. The yellow line is perpendicular to the brown line, the brown line is perpendicular to the blue line, and the blue line is perpendicular to the pink line. What conclusion can you make about the yellow line and the pink line? The yellow and the blue lines are parallel to each other because both are perpendicular to the brown line. Since the blue line is perpendicular to the pink line, then the pink line must be perpendicular to the yellow line by the Perpendicular Transversal Theorem.