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# Lesson 2.1 - PowerPoint PPT Presentation

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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Presentation Transcript

### 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

Τ

A

C

B

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

Τ

D

Given: AB BC

DC BC

Conclusion: <B = <C

Τ

Τ

~

C

B

Statement Reasons

• 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

~

~

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

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.

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.

C

60°

J

F

63°40’

30°

26°20’

D

E

G

H

<FGJ is the complement of <JGH.

<C is complementary to <E.

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.

2

A

B

C

Statement Reasons

• 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