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Contents
Angle Properties of straight lines
Angle Properties of Parallel Lines
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Properties of Parallel Lines
Activity
1 Draw 2 parallel lines. Then draw a line that cuts the 2 lines (transversal). ÐAPQ and ÐPQD are called alternate angels. ÐBPQ and ÐPQC are also alternate angles. Measure the angles with your protractor. What can you notice about alternate angles?
Activity
2
 In the
figure,
Ða and
Ðb are called
corresponding angles and
Ðb and
Ðc are called interior
angles on the same side of the transversal. What do
Ða and
Ðc add up to?
Do
Ðb
and
Ðc
add up to 180°?
The
above activities prove that
When a
transversal cuts two parallel lines,
(a) the
alternate angles are equal (alt.
Ðs)
(b) the
corresponding angles are equal (corr.
Ðs)
(c) the
interior angles on the same side of the transversal are supplementary angles
(int.
Ðs)
Two
lines in a plane are parallel of they are cut by a transversal in such a way
that
(a) the
alternate angles are equal, or
(b) the
corresponding angles are equal, or
(c) the
interior angles on the same side of the transversal are supplementary.
Example
1
  Find the value of x. Ða
= 180° - Ð x° (int. Ð
s, l3//l4)
3x° = a (alt. Ðs, l1//l2)
3x° = 180° - x°
4x° = 180°
x = 45
Example
2
 Find the angle x Draw a horizontal line parallel to l1 and l2 as
show.Ða = 180° - 120 °
 = 60° (supp. Ðs)
Ðb = 70° (corr. Ðs,
l2//l3)
Ðx = 60° + 70°
= 130°
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