2. Lines and Angles II

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Corresponding angles Corresponding angles

-- If If a ca cororrresespopondndiing ng ananglglee slid up (or down) slid up (or down) at theat the same side same sideof theof the transversal, then would find other corresponding angle.

transversal, then would find other corresponding angle.

∠

∠_{a =}_{a =} ∠∠_e_e ∠

∠_{c =}_{c =} ∠∠_g_g

-- WheWhen an F n an F dradrawn on wn on the the diadiagragram, tm, the cohe corrrrespespondionding anng anglegles cas can ben be found in the "corners" of the

found in the "corners" of the “F”“F”. . The F The F may may bebebackward and/or backward and/or upside-down. upside-down. D D P P Q Q e e a a g g c c A A B B f f b b ee aa d d h h _g_g cc B B AB is a transversal AB is a transversal Corresponding angles Corresponding angles ==

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Example 1 Example 1

In the diagram below find the value of In the diagram below find the value of y y

Solution Solution

∠

∠_{FEB =}_{FEB =} ∠∠_FDG_FDG _{(corresponding angle)}_{(corresponding angle)}

= 86 = 86oo x x ++ ∠∠_{FEB = 180}_{FEB = 180}oo x x + 86+ 86oo _{= 180}_{= 180}oo x x = 180= 180oo_{- 86}_{- 86}oo x x = 94= 94oo 2.

2. AlAlteternrnatate ane anglgleses

-- Alternate angles are equalAlternate angles are equal

A A B B f f b b ee aa d d h h _g_g cc d d c c b b a a x x 808 808 0 0 80 80 C C 86 86oo E E F F B B A A D D GG Alternater angles Alternater angles==

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-- Alternate angles Alternate anglescan be identified by the shape of thecan be identified by the shape of thecapital letter ‘Z’ capital letter ‘Z’ ..

Example 2 Example 2

Find the value of Find the value of yy

Solution Solution ∠ ∠_AEC_{AEC +}_{+ 107}₁₀₇oo _{= 180}_{= 180}oo ∠ ∠_{AEC = 180}_{AEC = 180}oo_{- 107}_{- 107}oo ∠ ∠_{AEC = 73}_{AEC = 73}oo y

y == ∠∠_AEC_AEC_{(alternate angle)}_{(alternate angle)} y

y = 71= 71oo

3.

3. InInteteririor or ananglgleses

The sum of interior angles is 180 The sum of interior angles is 180 OO

d d aa cc b b y y C C 107 107oo E E F F B B A A JJ GG H H

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∠

∠_{d +}_{d +} ∠∠_c_c_{= 180}_{= 180}OO

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

-- Interior angles are supplementary angles Interior angles are supplementary angles

Example 3 Example 3

Find the value of Find the value of zz

Solution Solution

zz + 59+ 59oo _{= 180}_{= 180}oo_{(sum of interior angles)}_{(sum of interior angles)}

z = 180 z = 180oo_{- 59}_{- 59}oo

z = 121 z = 121oo

Identifying parallel lines Identifying parallel lines

-- PrProperopertieties of ts of the anhe anglegles, prs, producoduced by ed by two stwo stratraighight lit lines cnes cut by ut by aa transversal, can used to identify whether the lines are

transversal, can used to identify whether the lines are parallel or not.parallel or not. cc d d aa b b zz 59 59oo

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1.

1. If AB iIf AB is a strs a straight laight line, detine, determinermine whethee whether line Sr line ST is paT is parallerallel to XYl to XY a) a) b) b) Solution Solution a) a) ∠ ∠_{SEB + 102}_{SEB + 102}oo = 180 = 180oo ∠ ∠_{SEB = 180}_{SEB = 180}oo_{- 102}_{- 102}oo ∠ ∠_{SEB = 58}_{SEB = 58}oo Given

Given ∠∠_{AFY = 58}_{AFY = 58}oo

∠

∠_{SEB =}_{SEB =} ∠∠_AFY_AFY _{(alternate angle)}_{(alternate angle)} Therefore, line ST is parallel to XY

Therefore, line ST is parallel to XY

S S B B X X Y Y S S A A 102 102oo 58 58oo E E FF X X D D S S Y Y T T B B A A 141 141oo 49 49oo C C

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∠

∠_ADX_ADX ≠≠ ∠∠_ACS_ACS_{(corresponding angle must be equal)}_{(corresponding angle must be equal)} Therefore, line ST is not parallel to XY

Therefore, line ST is not parallel to XY To master this chapter

To master this chapter •

• Do a lot of exercises.Do a lot of exercises. •

• Understand the concept of lines, parallel lines and transversal.Understand the concept of lines, parallel lines and transversal. Test yourself Test yourself A A B B 47 47

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1. 1.

In the diagram, AB is

In the diagram, AB is a straight line. The vala straight line. The value of x ue of x isis A A.. 447700 B B.. 994400 C C.. 11333300 D D.. 11337700 2. 2.

Find the value of y in diagram above. Find the value of y in diagram above.

A A.. 11990000 B B.. 22220000 C C.. 22330000 D D.. 22550000 3. 3.

Based on the diagram above, find the value of Based on the diagram above, find the value of y y-- x x ??

A A.. 444400

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Cancel Anytime. Answers Answers 1. 1. CC 2. 2. DD 3. 3. AA 4. 4. AA 5. 5. BB