1. TRIANGLE

2. 2
6
3
4 5
1
Which one is a triangle?

3. TYPES OF TRIANGLE

4. The types of triangles
1. Types of A Triangle Based on The Length of
The Sides
2. Types of A Triangle Based on The Measures
of The Angels
3. Types of A Triangle Based on The Angels and
The Sides

5. Types of Triangle Based on The Length
of The Sides
Do you still remember
about the types of
triangle based on the
length of the sides????
Equilateral
Triangle
Isosceles
Triangle
Scalene
Triangle
The types of triangle

6. Figure (a), the three sides of ΔABC have equal
lengths.
Figure (b) on ΔDEF, length of = length of side
.
Figure (c), the three sides of ΔPQR have different
lengths.
EF DF
What is the result
of your
measurement????

7. Measure the length of three sides of
each triangle

8. What is your
conclusion???
A triangle that all of its sides are Congruent is called
as an equilateral triangle
A triangle that has two congruent sides is called as an
isosceles triangle
A triangle that has nocongruent sides is called as a
scalene triangle

9. Types of Triangle Based on The
Measures of The Angles
Do you still remember
about the types of triangle
based on the measures of
the angles????
Acute Triangle Right Triangle Obtuse Triangle
The types of triangle

10. The definition:
A right triangle is a triangle that has one 90° angle
An acute triangle is a triangle that has three acute
angles
An obtuse triangle is a triangle that has one obtuse
angle.
Do you still remember
about the definition of each
types of triangle based on
the measures of the
angels???

11. Based on the pictures above, which ones is
right angle triangle, acute triangle and
obtuse triangle????

12. Types of A Triangle Based on The
Angles and The Sides
Do you still remember about
the types of a triangle based
on the angles and the
sides????
A right isosceles
triangle
An obtuse
isosceles triangle
An acute isosceles
triangle
The types of triangle

13. Definition :
• A right isosceles triangle is a triangle that has
one 90° angle and two equal sides.
• An obtuse isosceles triangle is a triangle that has
one obtuse angle and two equal sides.
• An acute isosceles triangle is a triangle that has
one acute angle and two equal sides.

14. Look at the following pictures!
Which one is a right isosceles triangle, an obtuse
isosceles triangle, and an acute isosceles triangle?????

15. SUM OF ANGLES
OF A TRIANGLE

16. Sum of Angles of a Triangle
Attention into ABC below!
What is sum of angles in the triangle? To
determine sum of the angles, do following task.

17. Task
1. Create a triangle paper ABC liked the previous
picture!
2. Mark CAB with number 1. ABC with number
2, and BCA with number 3. then, cut the three
angles liked the previous picture.
3. Arrange the result of cutting of angles number
1, 2, and 3 side by side as drawn liked previous
picture.
If you do the steps above are carefully, the
arrangement of the three cuts forms a straight
line. Therefore CAB + ABC + BCA =180˚

18. Sum of all angles in the
triangle is 180˚

19. Mathematically, the sum of all
angles in the triangle is 180˚. By
using properties of two parallel
lines intersected by other line, we
will prove the value.

20. In figure beside, PQ // AB,
line AR, BS, and PQ intersect
at C. Based on the properties
of two parallel line intersected
by any line, then we have the
followings.
a. ACB = SCR (due to
vertical angles)
b. BAC = QCR
(corresponding angles)
c. ABC = PCS
(corresponding angles)
Then, we have QCR + RCS +
SCP = QCP = 180˚
123
2
1 3
S
P Q
BA
R
C

21. Example
Determine the values of x, y, z if
AB // DE !
Solution :
See ABC! Sum of angles in ABC
is 180˚.
BAC + ABC + ACB = 180˚
30˚ + 40˚ + ACB = 180˚
ACB = 180˚- 70˚
= 110˚
y z
x
30˚
C
40˚
A B
ED

22. Since ACB and DCE are vertical each other,
then x = ACB = 110˚
Since BCA and CED are alternate,
then z = BAC = 30˚
Since ABC and CDE are alternate,
then y = ABC = 40˚
Value of y can also be determined using
x+y+z = 180˚ (remember that sum of angular
sizes in a triangles is 180˚)
110˚+ y + 30˚ = 180˚
y = 180˚ - 140˚ = 40˚

23. 1. Determine unknown angular sizes in following each triangle.
2. Determine value of x in the following triangles.
30˚
(a)
120˚ 35˚
(c)
40˚ 80˚
(b)
x
x
3x
5x
2x
x
x
70˚
(a) (b) (c)

24. PERIMETER AND
AREA OF
TRIANGLE

25. PERIMETER OF TRIANGLE
• Each plane must have perimeter.
• Perimeter of any plane is sum of length
bounding it.
• So we can conclude that:
Perimeter of Triangle
is sum of the length
of its sides

26. • Look at the figure
• In figure beside,
suppose perimeter is K
• AB = c, BC = a and
CA=b
B
C A
c
b
a
K = a+b+c
How about the Perimeter of
?ABC

27. THE AREA OF TRIANGLE
• Look at the figure
beside
• KLMN is a
rectangular where
is one of its
diagonals.
LN
K
MN
L

28. • Diagonals divides
the rectangular into to
two congruent right
triangle, namely
and .
• Since is
congruent to
then the areas of two
triangles are equal
LN
KLN MLN
KLN
MLN
K
MN
L
L KLMN = L + L
= 2 x L
L = x L KLMN
= x KL x KN
KLN
2
1
2
1
MLN
KLN
KLN

29. • Look at the figure
•Suppose that is
right triangle in K
•Line segment KL is base
of , while is
altitude of .
and are right sides of
right triangle KLN
KLN
KLN KL
KN
KN
K L
N
KLN

30. Now, look at the triangle
ABC in following picture
A
C
BD
A. = A. +A.
= ( x AD x
CD)+( x DB
x CD )
= x ( AD +
DB ) x CD
= x AB x CD
ABC ADC BDC
2
1
2
1
2
1
2
1

31. So, we can conclude that:
If the base of triangle is a ad the altitude
is t , area of triangle L is as follow.
taA
2
1

32. EXERCISE
In following figure, is a
right triangle on A
Determine:
a. L
b. L
ABC
ABC
BCD
D
B
CA
10cm
16 cm8 cm
26 cm

33. Draw
right, isosceles, or
equilateral triangle

34. Draw right triangle
Suppose we will draw a right triangle ABC. To
draw the right triangle, follow these steps.
1. Draw AB
2. From A, draw a perpendicular line AC with
AB. The size of length is an arbitrary length
(AB<AC, AB=AC, AB<AC)
3. Connect C to B, so we obtain a right triangle.

35. Illustration
A B
C
A B A B
C