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Lesson 2.1. Complements & Supplements. Perpendicularity. Lesson 2.2. Perpendicular: lines, rays or segments that intersect at right angles. Symbol for perpendicular. Τ. X. B. b. A. B. a. A. D. Y. AB. Τ. BD. a. Τ. b. XY. Τ. AB. If <B is a right angle, then AB BC. Τ. A.

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Lesson 2.1

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Lesson 2.1

Complements & Supplements

Perpendicularity

Lesson 2.2

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

Symbol for perpendicular

Τ

X

B

b

A

B

a

A

D

Y

AB

Τ

BD

a

Τ

b

XY

Τ

AB

If <B is a right angle, then AB BC

Τ

A

C

B

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

Τ

A

D

Given: AB BC

DC BC

Conclusion: <B = <C

Τ

Τ

~

C

B

StatementReasons

• AB BC

• <B is a right <.

• DC BC

• <C is a right <.

• <B = <C

Τ

• Given

• If 2 segments are , they form a right <.

• Given.

• If 2 segments are , they form a right <.

• If <‘s are right <‘s, they are =.

Τ

Τ

Τ

~

~

J

Given: KJ KM

<JKO is 4 times as large as <MKO

Find: m<JKO

Τ

O

4x°

M

K

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

y axis

Given: EC ll x axis

CT ll y axis

Find the area of RECT

C (7, 3)

E

321

123

x axis

-3 -2 -1 1 2 3

R (-4,-2)

T

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)

=55

The area of RECT is 55 square units.

Complementary Angles

40°

A

B

50°

<A & <B are complementary.

Complementary angles are two angles whose sum is 90°.

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

More Complementary Angles

C

60°

J

F

63°40’

30°

26°20’

D

E

G

H

<FGJ is the complement of <JGH.

<C is complementary to <E.

Supplementary Angles

130°

K

50°

J

<J & <K are supplementary.

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

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

1

2

A

B

C

StatementReasons

• Diagram as shown.

• <ABC is a straight angle.

• <1 is supplementary to <2.

• Given

• Assumed from diagram

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

Given: Diagram as shown

Conclusion: <1 is supplementary to <2