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Lines and Angles
Calter, Section 6-1
Define the following terms:
Line
Line segment
Angle
Vertex
Perpendicular lines
Parallel lines
In the picture to the right, we can designate the angle in any of the following ways:
angle ABC
angle CBA
angle B
angle θ
We can also use the symbol
 or
to mean ‘angle’
i) Draw and define an acute angle ABC .
ii) Draw and define an right angle DEF .
iii)Draw and define an obtuse angle GHI .
iv) Draw and define a straight angle JKL .
v) Draw and define complementary angles.
vi) Draw and define supplementary angles.
Lines, Angles and Triangles
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Angles between intersecting lines
In the figure, which angles are equal? Which angles are supplementary?
Parallel lines
There are certain angle properties that apply ONLY to parallel lines.
If there are two parallel lines intersected by a third line p, the line p is called the transversal.
In the figure, which angles are equal. Which angles are supplementary?
Triangles
Calter, Section 6-2
Draw and define the following triangles by angle measure:
i) Right triangle
ii) Acute triangle
iii) Obtuse triangle
Lines, Angles and Triangles
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Draw and define the following triangles by side length:
i) Scalene triangle
ii) Acute triangle
iii) Equilateral triangle
Define the Sum of the Interior Angles in a triangle property:
Define the Exterior angle of a Triangle property:
Define the Isosceles Triangle Theorem:
Congruent Triangles
Two triangles (or any other polygons, for that matter) are said to be congruent if the angles and
sides of one are equal to the angles and sides of the other.
We can say that 2 triangles are congruent if they satisfy one of the following conditions:
- Two sides and the contained angle of one triangle equal two sides and the contained
angle of the other triangle (“Side-Angle-Side Theorem”)
- Two angles and any side of one triangle are equal to two angles and the contained side of
the other triangle (“Angle-Angle-Side Theorem”)
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Similar Triangles
Two triangles are said to be similar if they have the same shape, even if one triangle is larger
than the other. The angles of one of triangle must equal the angles of the other triangle. Their
sides will be proportional.
Polygons
Define the Sum of the Interior Angles of a Polygon Theorem:
Practise
Find the measures of all the angles in the figures below:
1)
2)
a
65º
b
c
z
d
3)
e
y
f
z
4)
70º
g
h
j
l
z
i
k
zm
35º
z
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5)
6)
70o
58o
15 cm
9 cm
3 cm
30o
4 cm
7. In question 6, find the lengths of all the sides
8. If two angles in a triangle measure 34 and 65 degrees, what is the measure of the third angle?
9. Joseph wishes to find the length of a lake. He makes the measurements shown. Calculate the
length of the lake.
65 m
52 m
65o
72 m
65o
10. CHALLENGE: Tina wants to find the height of a tree. She places a meter stick vertically on
the ground and notices that the stick casts a shadow 0.4m long. The tree casts a shadow 2m
long. How high is the tree?
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