Lesson 2.1Lesson 2.1

PerpendicularityPerpendicularity

Complements & Complements & SupplementsSupplements

Lesson 2.2Lesson 2.2

Perpendicular: lines, rays or segments that intersect at right angles.

Τ

Symbol for perpendicular

Τ

a b

a

b

AD

B

AB BD

X

Y

A B

XY AB

ΤΤ

If <B is a right angle, then AB BC

Τ

C

A

B

Can’t assume unless you have a right angle or given.

Τ

A

C

D

B

Given: AB BC

DC BC

Conclusion: <B = <C~

Τ

Τ

Statement Reasons

1. AB BC2. <B is a right <.

3. DC BC4. <C is a right <.

5. <B = <C

Τ

1. Given2. If 2 segments are ,

they form a right <.3. Given. 4. If 2 segments are ,

they form a right <.5. If <‘s are right <‘s,

they are =.

Τ

Τ

Τ

~~

Given: KJ KM

<JKO is 4 times as large as <MKO

Find: m<JKO

Τ

M

J

K

O

x°4x°

Solution:

Since KJ KM, m<JKO + m<MKO = 90°.

4x + x = 90 5x = 90 x = 18

Substitute 18 for x, we find that m<JKO = 72°.

Τ

Given: EC ll x axis

CT ll y axis

Find the area of RECT x axis

y axis

-3 -2 -1 1 2 3

321

123

C (7, 3)

T R (-4,-2)

E

Solution:The remaining coordinates are T = (7, -2) and E = (-4, 3). So RT = 11 and TC = 5 as shown. Area = base times height.A = bh = (11)(5) =55The area of RECT is 55 square units.

Complementary AnglesComplementary Angles

Complementary angles Complementary angles are two are two angles whose sum is 90°.angles whose sum is 90°.

Each of the two angles is called the Each of the two angles is called the complement complement of the other.of the other.

A B40°

50°

<A & <B are complementary.

More Complementary AnglesMore Complementary Angles

<C is complementary to <E.<C is complementary to <E.

D E

C

60°

30°

F

G

J

H

63°4

0’

26°20’

<FGJ is the complement of <JGH.

Supplementary AnglesSupplementary Angles Supplementary angles Supplementary angles are two are two

angles whose sum is angles whose sum is 180° 180° (a straight (a straight angle). angle).

Each of the two angles is called the Each of the two angles is called the supplementsupplement of the other. of the other.

JK130° 50°

<J & <K are supplementary.

Given: Diagram as shownGiven: Diagram as shown

Conclusion: <1 is supplementary to <2Conclusion: <1 is supplementary to <2

A B C

1 2

Statement Reasons

1. Diagram as shown.2. <ABC is a straight

angle.3. <1 is supplementary

to <2.

1. Given2. Assumed from diagram

3. If the sum of two <‘s is a straight <, they are supplementary.