1. BY IGOR ANDRZHIEVSKY, CHRIS FERRARIO, AND ANDREW REBENSKY Section 2.1-Perpendicularity

2. What Are Perpendicular Lines? As we learned earlier, right angles are 90 degrees. Perpendicular- Lines, rays, or segments that intersect at right angles. The symbol for perpendicularity is A A Examples: B 90 O 90 O D B 90 O C C Section 2.1 Perpendicularity

3. Identifying Perpendicular Lines Section 2.1 Perpendicularity In diagrams, perpendicular lines will be clearly shown. Don’t ever assume that lines are. If you see an angle with a box then it is a right angle. Possible diagrams of perpendicular lines are…. A Good Bad W X B C Z Y There is no sign in this figure that any lines are perpendicular.

4. Perpendicular Theorems Section 2.1 Perpendicularity Theorems: If lines, segments, or rays intersect to form right angles then they are perpendicular. (For proving perpendicular lines with having right angles) If lines, segments, or rays are perpendicular, then they form right angles. (For proving right angles with having perpendicular lines) Perpendicular lines form right angles. (Short form for proving right angles with having perpendicular lines) Right angles are formed by perpendicular lines. (Short form converse for proving perpendicular with having right angles already)

5. A Review of Coordinate Planes Section 2.1 Perpendicularity y-axis Coordinates are a point‘s ordered pair from its location from the origin (x,y). x-axis That point is called the origin. Its coordinates are (0,0).

6. Oblique Lines Section 2.1 Perpendicularity Oblique lines are another form of intersecting lines. Oblique lines: Two lines that intersect and are not perpendicular. Examples: F A D 25 o 89 o 91 o 155 o E 155 o I J G 25 o 91 o 89 o B C H

7. Sample Problems Section 2.1 Perpendicularity Question 1 A B E F G H D C Given: and Prove:

8. Sample Problems Continued Section 2.1 Perpendicularity Answer 1 Statement Reasons 1. 1. Given 2. 2. Given 3. are 3. Perpendicular lines right angles form right angles 4. 4. Right angles are congruent

9. Sample Problems Continued Section 2.1 Perpendicularity Question 2 J K y 4y N L M Given: Find: y

10. Sample Problems Continued Section 2.1 Perpendicularity Answer 2 so are right angles because perpendicular lines form right angles. This means that they both equal 90 degrees because that’s what right angles equal. By addition, 5y (4y+y=5y) is congruent to 90 degrees. 5y=90.

11. Practice Problems Section 2.1 Perpendicularity Question 1 A B C Given: =(2x) E D =(x-6) Find: m

12. Practice Problems Continued Section 2.1 Perpendicularity Answer 1 Since we know that is a right angle because perpendicular lines form right angles. Right angles are 90 degrees. plus will equal 90 degrees 2x + (x-6)= 90 3x= 96 x= 32 m = 64

13. Practice Problems Continued Section 2.1 Perpendicularity Question 2 I A R G O Given: ; trisect ; Find:

14. Practice Problems Continued Section 2.1 Perpendicularity Answer 2 Since, we know that is a right angle because perpendicular lines form right angles. From there it says that trisect the big angle. Trisecting rays divide the angle into three congruent smaller angles. So, 90 degrees trisected or divided by three is 30. is one of the three smaller angles so it equals 30 degrees. m =30

15. Works Cited Section 2.1 Perpendicularity "Automotive Dictionary - "TI."" Motor Era. Automobile History. 2008. Web. 19 January, 2011. Minick, Laurie, and Lydia Priest. "Perpendicular." Picture This! Instructional Strategeaze. 8 Feb. 2010. Web. 19 January, 2011. Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Fun and Challenge. New Edition ed. Evanston, Illinois: McDougal Litell, 1991. Print. 16 January, 2011. Tashian, Carl. "Fool's Tools Archives." Killer Runway Design. 12 Sept. 2006. Web. 19 January, 2011