Triangle Basics
Parts of a Triangle
A
• Sides
Segment
AB, AC, BC
Vertices
Points
A, B, C
B
Angles
Angles
A, B, C
C
Classification by Angles
•Acute
•Obtuse
•Right
•Equiangular
Classification by Sides
•Scalene
•Isosceles
•Equilateral
Interior angles of a Triangle
The interior angles of a triangle always add up to 180°!
Congruent Triangles
Exercise 8.10
What does Congruent Mean?
• Two objects are congruent if they have the same
dimensions and shape. Very loosely, you can think of
it as meaning ‘EQUAL’.
Two LINES are congruent if they
have the same length.
Two ANGLES are congruent if
they have the same value.
Congruent Triangles
• Congruent Shapes have an equal number of sides,
and all the corresponding sides and angles are
congruent.
• However, they can be in a different location, rotated
or flipped over.
So for example the two
triangles shown on the right
are congruent even though
one is a mirror image of the
other
Conditions for Congruency of Triangles
Three sides equal. (SSS)
Two sides and the included angle equal. (SAS)
Two angles and a corresponding side equal . (AAS)
Right angle, hypotenuse and side (RHS)
Which congruency do these triangles
represent:
SAS, AAS, SSS or RHS?
SIDE –ANGLE – SIDE (SAS)
SIDE –SIDE – SIDE (SSS)
ANGLE–ANGLE – SIDE (AAS)
RIGHT–HYPOTENUSE– SIDE (RHS)
SSS
SAS
Decide which of the triangles
are congruent to the red
triangle, giving reasons.
10 cm
SAS
1

8 cm
25o
35o
35o
120o
2

120o
3


SSS
10 cm
10 cm
4 cm
AAS
RH
4 cm S
10 cm
8 cm
4 cm
AAS
4
120o
8 cm
8 cm
35o
4 cm
120o
SAS
5
Not to Scale!

25o
8 cm
35o

120o
6
SSS
SAS
AAS
Decide which of the triangles
are congruent to the yellow
triangle, giving reasons.
1
2
5 cm

13 cm
13 cm
13 cm

4
5 cm
20o
20o
5
3
70o
13 cm
5 cm
Not to Scale!
70o
AAS

12 cm

12 cm
RH
S
12 cm
SSS
RH
S
20o
13 cm
RH
S

13 cm
70o
13 cm
SAS

5 cm
6
Similar Triangles
Exercise 8.11
Similar Triangles
• Two Triangles that have two angles that are the same in
size are know as SIMILAR
• Similar triangles may be different in size but
corresponding side lengths can always be calculated as
the same ratio
Corresponding Ratios
90 ÷ 45 = 2
80 ÷ 40 = 2
100 ÷ 50 = 2
What is the ratio between each of
these congruent triangle pairs
1. Find the similar side - 4cm and 8 cm
2. Find the ratio
8cm ÷ 4cm = 2
3. Find the similar side for x
2cm side
4. Use the ratio to calculate X
2cm x 2 (Ratio) = X
X = 4cm
1. Find the similar side - 6cm and 18 cm
2. Find the ratio
18cm ÷ 6cm = 3
3. Find the similar side for x
6cm side
4. Use the ratio to calculate X
6cm ÷ 3 (Ratio) = X
X = 2cm
Harder Examples:
B
1. Find the two similar triangles:
i.
Triangle ABC
ii. Triangle ADE
D
A
E
1.5cm+ 2.5cm = 4cm
C
2. Find the similar sides
i.
4cm and the 1.5cm
ii. X and 1.2cm
3. Calculate the Ratio:
i.
4cm ÷ 1.5cm = 2.6
4. Calculate the X value:
i.
1.2cm x 2.6 (ratio) =
3.2cm
Lets try this example