Chapter 1 lines and angles ii [compatibility mode]
-
Upload
khusaini-majid -
Category
Education
-
view
197 -
download
1
Transcript of Chapter 1 lines and angles ii [compatibility mode]
2
1.1 PROPERTIES 1.1 PROPERTIES 1.1 PROPERTIES 1.1 PROPERTIES
OF ANGLES OF ANGLES OF ANGLES OF ANGLES
ASSOCIATED ASSOCIATED ASSOCIATED ASSOCIATED
WITH WITH WITH WITH
TRANSVERSALS TRANSVERSALS TRANSVERSALS TRANSVERSALS
AND PARALLEL AND PARALLEL AND PARALLEL AND PARALLEL
LINESLINESLINESLINES
3
Transversal
– a line that intersects two or more parallel lines
Identify transversals, corresponding angles, Identify transversals, corresponding angles, Identify transversals, corresponding angles, Identify transversals, corresponding angles,
alternate angles and interior anglesalternate angles and interior anglesalternate angles and interior anglesalternate angles and interior angles
P
QQQ
S
RPP
PQ and RS are transversals.
4
Corresponding angles
e
f
d
c
abTIPS
Corresponding angles
can be identified by
the F shape. The F can
be flipped over or
turned upside down.Shaded angles are
corresponding angles. Angles a
and d are also corresponding
angle.
5
Alternate angles
Shaded angles are alternate angles.
Angles a and b also alternate angles.
TIPS
Alternate angles can
be identified by the Z
shape or Z shape.
6
Interior angles
Shaded angles are interior angles.
Angles c and d also interior angles.
TIPS
Interior angles can be
identified by the Z
shape or Z shape.
7
Corresponding angles are equal
Determine that for parallel lines: Determine that for parallel lines: Determine that for parallel lines: Determine that for parallel lines:
a) corresponding angles are equala) corresponding angles are equala) corresponding angles are equala) corresponding angles are equal
8
Determine that for parallel lines: Determine that for parallel lines: Determine that for parallel lines: Determine that for parallel lines:
b) alternate angles are equalb) alternate angles are equalb) alternate angles are equalb) alternate angles are equal
Alternate angles are equal
9
Determine that for parallel lines: Determine that for parallel lines: Determine that for parallel lines: Determine that for parallel lines:
c) the sum of interior angles is 180c) the sum of interior angles is 180c) the sum of interior angles is 180c) the sum of interior angles is 180°°°°
The sum of interior angles is 180° or interior angles are supplementary
10
Exercise 1.1AExercise 1.1AExercise 1.1AExercise 1.1A
1. For each of the following diagrams, list
i. four pairs of corresponding angles.
ii. two pairs of alternate angles.
iii. two pairs of interior angles.
a) b)
11
Find the value of x in each of the following.
a) b)
Find the values of corresponding angles, Find the values of corresponding angles, Find the values of corresponding angles, Find the values of corresponding angles,
alternate angles and interior angles, alternate angles and interior angles, alternate angles and interior angles, alternate angles and interior angles,
associated with parallel linesassociated with parallel linesassociated with parallel linesassociated with parallel lines
Example 1Example 1Example 1Example 1
12
a) The angles shown in the diagram are
corresponding angles.
Corresponding angles are equal.
Thus, x = 125°.
b) The angles shown in the diagram are interior
angles.
The sum of interior angles is 180°.
Thus, x + 74° = 180°
x = 180° - 74° = 106°
Solution:
13
Exercise 1.1BExercise 1.1BExercise 1.1BExercise 1.1B
Find the value of the unknown in each of the
following.
1. 2.
3. 4.
14
When two straight lines are intersected by a
transversal, and
Determine if two given lines are parallel Determine if two given lines are parallel Determine if two given lines are parallel Determine if two given lines are parallel
based on the properties of angles associated based on the properties of angles associated based on the properties of angles associated based on the properties of angles associated
with transversalswith transversalswith transversalswith transversals
• if the corresponding angles are equal, then the
two lines are parallel.
• if the alternate angles are equal, then the two
lines are parallel.
• if the interior angles are supplementary, then
the two lines are parallel.
15
Example 2Example 2Example 2Example 2
In the diagrams below, KLM, STU and LTV are
straight lines. Determine if the lines KLM and
STU are parallel.
a) b)
16
a) The corresponding angles are equal.
Thus, the lines KLM and STU are parallel.
b) If the lines are parallel,
then, LTU = 153°.
Given STU is a straight line.
Hence, STU = 180°.
But LTU + LTS = 153° + 26°
= 179° ≠ 180°
Thus, the lines KLM and STU are not parallel.
Solution:
Corresponding angle
17
Exercise 1.1CExercise 1.1CExercise 1.1CExercise 1.1C
1. Determine if the bold lines shown below are
parallel.
a) b)
19
The diagram shows a parallelogram ABCD. Given
EDC is a straight line. Calculate all the angles in
the parallelogram.
Solve problems involving the properties of Solve problems involving the properties of Solve problems involving the properties of Solve problems involving the properties of
angles associated with transversalsangles associated with transversalsangles associated with transversalsangles associated with transversals
20
DCB = EDA
= 105°
ADC = 180° - DCB
= 180° - 105°
= 75°
DAB = EDA
= 105°
ABC = 180° - DAB
= 180° - 105°
= 75°
Solution:
Alternate angles
Interior angles
Corresponding angles
Interior angle
21
Example 4Example 4Example 4Example 4
The diagram shows two parallel lines intersected
by two transversals. Find the values of x and y.
22
BSV = ABS
x = 34°
Angle y is the sum of ASW and WSC.
ASW = 180° - UAS
= 180° - 93°
= 87°
WSC = UBS
= 34°
Thus, y = 87° + 34°
= 121°
Solution:
23
Exercise 1.1DExercise 1.1DExercise 1.1DExercise 1.1D
1. In the diagram, ABCD is a trapezium and the
line EF is an extension of AB. Given EAD
= 77° and FBC = 25°. Calculate all the
angles in the trapezium.
25
Summary Summary Summary Summary LINES AND ANGLES IILINES AND ANGLES IILINES AND ANGLES IILINES AND ANGLES II
Parallel lines
* The lines that will never meet
* The lines that are always the same
distance apart.
Transversal
* A line that intersects two or
more parallel lines.
Transversal and parallel lines
Corresponding angles
* are equal
* can be identified by the
F shape.
Corresponding angles
Alternate angles
* are equal
* can be identified
by the Z shape.
Interior angles
* have a sum of 180°
* can be identified
by the UUUU shape.
Interior anglesAlternate angles