Properties of Triangles 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 equalto the sum of the interior opposite angles.

Use angle properties of isosceles, equilateral and right-angled triangles.

Properties of Triangles Properties of Triangles

What do these symbols mean?

right angle parallel toeach other

parallel to each other,but not parallel with the sides with only one arrow

same lengthas each other

same length as each other, but not the same length as the sides with only one dash

Properties of Triangles Properties of Triangles

Isosceles:

2 sides the same length2 angles the same

What are the names and properties of these triangles ?

Equilateral:

All sides the same lengthAll angles the same (60o)

Right-angled:

Sides can be any lengthOne angle 90o

Scalene:

All the sides are different lengthsAll the angles are different

Properties of Triangles 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?

Properties of Triangles Properties of Triangles

Proof that the internal angles in a triangle add up to 180o

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 anglesare now on a

straight line and therefore mustadd up to 180o

Properties of Triangles Properties of Triangles

a = 180 – (80+30) = 70

Now do these:

30o

80o

a

41o

54o

b 62o 34o

c

141o x y z

58o

79o

r

q p57o

b = 180 – (54+41) = 85

c = 180 – (62+34) = 84

x = 180 – 141 = 39

y = 180 – (58+39) = 83z = 180 – 83 = 97

p = 180 – (90+57) = 33

q = 57 (vertically opposite angles are equal)

r = 180 – (79+57) = 44

Properties of Triangles Properties of Triangles

a

c

b

68o

39o d

e

46o 17o

a = 180 – 90 = 90b = 180 – (90+39) = 51c = 180 – (90+68) = 22

d = 180 – (90+46) = 44

e = 180 – (90+44+17) = 29

Think big triangle