concept of triangles and properties_1.ppt

mathematics concepts

2. Properties of Triangles
Objectives:
G Grade Identify isosceles, equilateral and right-angled
triangles.
Use the word ‘congruent’ when triangles are
identical.
E Grade Show that the angles of a triangle add up to 180
o
and use this to find angles.
Show that the exterior angle of a triangle is equal
to the sum of the interior opposite angles.
Use angle properties of isosceles, equilateral
and right-angled triangles.

3. Properties of Triangles
What do these symbols mean?
right angle
parallel to
each other
parallel to each other,
but not parallel with
the sides with only
one arrow
same length
as each other
same length as each
other, but not the same
length as the sides with
only one dash

4. Properties of Triangles
Isosceles:
2 sides the same length
2 angles the same
What are the names and properties of these triangles ?
Equilateral:
All sides the same length
All angles the same (60
o
)
Right-angled:
Sides can be any length
One angle 90
o
Scalene:
All the sides are different lengths
All the angles are different

5. Properties of Triangles
Congruent: means all angles and lengths are the same.
It can be a rotation
a
b
c
d
e
f
g
h
i
j
Which shapes are congruent?

6. Properties of Triangles
Proof that the internal angles in a triangle add up to 180
o
a
a
b
b
a
b
Alternate angles are equal
Add a line parallel to one of the sides
Corresponding angles are equal
The internal angles
are now on a
straight line and
therefore must
add up to 180
o

7. Properties of Triangles
a = 180 –(80+30)
= 70
Now do these:
30
o
80
o
a
41
o
54
o
b 62
o 34
o
c
141
ox y
z
58
o
79
o
r
q
p
57
o
b = 180 –(54+41)
= 85
c = 180 –(62+34)
= 84
x= 180 –141 = 39
y= 180 –(58+39)
= 83
z= 180 –83 = 97
p= 180 –(90+57) = 33
q= 57
(vertically opposite
angles are equal)
r= 180 –(79+57) = 44

8. Properties of Triangles
a
c
b
68
o
39
o
d
e
46
o17
o
a= 180 –90 = 90
b= 180 –(90+39) = 51
c= 180 –(90+68) = 22
d= 180 –(90+46) = 44
e= 180 –(90+44+17) = 29
Think big triangle

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