Transcript Document
Objectives: E Grade
Properties of Triangles
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.
Properties of Triangles
Using the symbols describing shapes answer the following questions:
b
45 o 36 o
a c
Isosceles triangle Two angles are equal
a
= 36 o
b
= 180 – (2 × 36) = 108 o Equilateral triangle all angles are equal
c
= 180 ÷ 3 = 60 o Right-angled triangle
d d
= 180 – (45 + 90) = 45 o
Example
p r
Properties of Triangles
q
Made up of 2 isosceles triangles 36 o
s p
= 38 o
q
= 180 – (2 × 38) = 104 o 56
+
(r + s) = 180 o (r + s) = 180 – 56 = 124 Because
r
=
s r
=
s =
124 ÷ 2 = 62 o 56 o
Now do these:
Properties of Triangles
a
= 64 o
b
= 180 – (2 ×64 o ) = 52 o
c
=
d c c c
+
d =
180 - 72 +
d =
108 =
d =
54 o Equilateral triangle
e
=
f
=
g
= 60 o
h
=
i h c h
+
i =
180 - 90 + i
=
90 =
d =
45 o
p
= 50 o
q
= 180 – (2 ×50 o ) = 80 o
r
=
q =
80 o
vertically opposite angles are equal
Therefore :
s = t = p =
50 o
Properties of Triangles
e
=
f
=
g
= 60 o
d
= 180 – 60 = 120 o
e +
18
= a
= 60
external angle = sum of opposite internal angles e
= 60 – 18 = 42 o
p
=
q
=
r
= 60 o
s
= t = 180 - 43 = 68.5
o 2