Transcript Document

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 180o
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.
Properties of Triangles
What do these symbols mean?
right angle
parallel to
each other
same length
as each other
parallel to each other,
but not parallel with
the sides with only
one arrow
same length as each
other, but not the same
length as the sides with
only one dash
Properties of Triangles
What are the names and properties of these triangles ?
Isosceles:
Equilateral:
Right-angled:
2 sides the same length
2 angles the same
All sides the same length
All angles the same (60o)
Sides can be any length
One angle 90o
Scalene:
All the sides are different lengths
All the angles are different
Properties of Triangles
Congruent: means all angles and lengths are the same.
It can be a rotation
e
j
a
g
f
d
b
i
h
c
Which shapes are congruent?
Properties of Triangles
Proof that the internal angles in a triangle add up to 180o
a
b
Add a line parallel to one of the sides
Alternate angles are equal
a
The internal angles
are now on a
straight line and
therefore must
add up to 180o
b
Corresponding angles are equal
Properties of Triangles
Now do these:
41o
80o
30o
c
b = 180 – (54+41) c = 180 – (62+34)
= 85
= 84
79o
y z
x
34o
62o
54o
a
a = 180 – (80+30)
= 70
141o
b
q
57o
58o
x = 180 – 141 = 39
y = 180 – (58+39)
= 83
z = 180 – 83 = 97
p
p = 180 – (90+57) = 33
r
q = 57
(vertically opposite
angles are equal)
r = 180 – (79+57) = 44
Properties of Triangles
68o
e
a
c
b
39o
a = 180 – 90 = 90
b = 180 – (90+39) = 51
c = 180 – (90+68) = 22
46o
17o
d
d = 180 – (90+46) = 44
Think big triangle
e = 180 – (90+44+17) = 29