TRIANGLE

2

6

3

4 5

1

Which one is a triangle?

TYPES OF TRIANGLE

1

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

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

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????

Measure the length of three sides of each triangle

What is your conclusion???

A triangle that all of its sides are Congruent is called as an equilateral triangleA triangle that has two congruent sides is called as an isosceles triangleA triangle that has nocongruent sides is called as a scalene triangle

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

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???

Based on the pictures above, which ones is right angle triangle, acute triangle and

obtuse triangle????

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

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.

Look at the following pictures!

Which one is a right isosceles triangle, an obtuse isosceles triangle, and an acute isosceles triangle?????

(2)

(3)A

C

B

SUM OF ANGLES OF A

TRIANGLE2

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.

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˚

Sum of all angles in the triangle is 180˚

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.

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

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 zx

30˚

C

40˚A B

ED

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˚

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

3x5

x

2x

x

x

70˚

(a) (b) (c)

EXERCISE

PERIMETER AND AREA OF TRIANGLE

3

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

• 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

THE AREA OF TRIANGLE

• Look at the figure beside

• KLMN is a rectangular whereis one of its diagonals.

LNK

MN

L

• 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 MLNKLN

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

KLNKLN

• 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

KLNKLN KL

KN

KN K L

N

KLN

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

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

EXERCISE

In following figure, is a right triangle on A

Determine:a. L b. L

ABC

ABC

BCD

D

B

CA

10 c

m

16 cm8 cm

26 cm

Draw right, isosceles, or equilateral triangle

4

Draw right triangle

Suppose we will draw a right triangle ABC. To draw the right triangle, follow these steps.1. Draw AB2. 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.

Illustration

A B

C

A B A B

C