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

BY IGOR ANDRZHIEVSKY, CHRIS FERRARIO, AND ANDREW REBENSKY

Section 2.1-Perpendicularity

Section 2.1 Perpendicularity

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 90O 90O

D

B 90O

C C

BCBA

BDAC


Identifying Perpendicular Lines

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

BCAB ZYWZ

There is no sign in this

figure that any lines

are perpendicular.


Perpendicular Theorems

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)


A Review of Coordinate Planes

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).


Oblique Lines

Oblique lines are another form of intersecting lines.Oblique lines: Two lines that intersect and are not

perpendicular. Examples: F A D 25o 89o 91o

155o E 155o I J G

25o 91o 89o

B C H


Sample Problems

Question 1 A B E

F

G H

D C

Given: and Prove:

CDAD HGEG EGHADC


Sample Problems Continued

Answer 1 Statement Reasons1. 1. Given2. 2. Given 3. are 3. Perpendicular

lines right angles form right angles4. 4. Right angles are congruent

CDAD HGEG EGHADC ,

EGHADC



Question 2 J K

y

4y

N L

MGiven: Find: y

NLMJ



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.

NLMJ JMNJML ,

y=18


Practice Problems

Question 1 A B C

Given:

=(2x) E D

=(x-6)Find: m

EDBE

CEDBEC

CED


Practice Problems Continued

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

EDBE BED

CED BECCED

m = 64CED



Question 2 I A R

G OGiven: ; trisect ;Find:

GOGI GRGA, IGO

AGR



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.

GOGI

GRGA,

IGO

AGR

m =30AGR


Works Cited

"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

Documents

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