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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
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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.