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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°

x°

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.

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.

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