2. Lines and Angles II

Lines and Angles II  By Muralle Do you Know? This chapter continues from Form 1, Chapter 9. • Will be tested only in Paper 1. • Tested 2004 – 2008 except year 2007. • The main concepts in Form 3 are parallel lines, transversals, corresponding • angles, alternate angles and interior angles. Properties of angles associated with transversals and parallel lines 1. Transversal  – a line that intersect  two or more parallel lines

transversal 

A

 AB is a transversal 

B Corresponding angles - If a cor corrrespo espond ndiing angl anglee slid up (or down) at the same side of the transversal, then would find other corresponding angle.

P a c

Corresponding angles =

“F”

search for letter 

e g

Q ∠a = ∠e ∠c = ∠g

-

When When an F drawn drawn on the diagra diagram, m, the the corr corresp espondi onding ng angle angless can can be found in the "corners" of the “F”. The F may be backward and/or  upside-down. A a d e h

 b c

f  g

B D

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A a d e h

 b c

f  g

B

 Example 1  y In the diagram below find the value of  y F  x  A B E 808 0 86o 80 D G C

Solution ∠FEB

= ∠FDG (corresponding angle) = 86o  x + ∠FEB = 180o  x + 86o = 180o  x = 180o - 86o  x = 94o

2. Alte Altern rnat atee angl angles es - Alternate angles are equal

a c

d

b

  Alternater angles=

“Z”

search for letter 

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-

 Alternate angles can be identified by the shape of the capital letter ‘Z’ .

a d

 b c

 Example 2 Find the value of y F o

107

A

B

E  y

J

H

G

C Solution o o ∠AEC + 107 = 180 o o ∠AEC = 180 - 107 o ∠AEC = 73

 y = ∠AEC (alternate angle)  y = 71o

3. Inte Interi rior or angl angles es The sum of interior angles is 180

O

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∠d + ∠c = 180 O

-

 Interior angles can be identified by the shape of capital letter ‘U’ 

a  b

d c

-

 Interior angles are supplementary angles

 Example 3 Find the value of z z

59o Solution z + 59o = 180o (sum of interior angles) z = 180o - 59o z = 121o Identifying parallel lines - Proper Propertie tiess of the the angle angles, s, produc produced ed by two stra straigh ightt lines lines cut cut by a transversal, can used to identify whether the lines are parallel or not.

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 Example 4 1. If AB is is a straight straight line, line, determin determinee whether whether line ST ST is paralle parallell to XY a) S X

102o A

58o

E

S

B

F

Y

S

X 49o

 b)

B

D

141o A

C T

Y

Solution a)

+ 102o = 180o o o ∠SEB = 180 - 102 o ∠SEB = 58 Given ∠AFY = 58o ∠SEB = ∠AFY (alternate angle)

∠SEB

Therefore, line ST is parallel to XY

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Given ∠ACS = 141o ∠ADX ≠ ∠ACS (corresponding angle must be equal) Therefore, line ST is not parallel to XY To master this chapter Do a lot of exercises. • Understand the concept of lines, parallel lines and transversal. • Test yourself 

A

47

B

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1.

In the diagram, AB is a straight line. The value value of x is 0 A. 47 B. 940 C. 1330 D. 1370 2.

Find the value of y in diagram above. A. 1900 B. 2200 C. 2300 D. 2500 3.

Based on the diagram above, find the value of  y  y - x ? 0 A. 44

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Answers 1. C 2. D 3. A 4. A 5. B