EQUAL TRIANGLES

1

The sides are 3cnههههه

Introduction

A Triangle, you have seen is a simple closed curve Made of three line segments.

A B

C

If the lengths of the sides of a triangle are given, you know how to draw it .The sides are 3centimetres,5centimetres,6centimetres.

3cm

6cm

5cm

3cm

6cm

5cmor

Now draw with the 5centimetres Base:

5cm

3cm

6cm

3cm

5cm

6cm

or

n

Similarly draw the triangles with base 6. in all six triangles ,sides are equal. Each pair of triangle are called equal triangle.

If the sides of a triangle are equal to the sides of another triangle, then these triangle are equal

According to Euler

Now looking at all these 6 triangles what about angles?

By coincide all triangles ,When equal sides coincides angles also coincide ,Don’t they?

Check it out on another set.

Let's down a general principle, we have

If the sides of a triangle are equal to the sides of another triangle, Then the angles of the triangles are also equal.

n

Look at these triangles and

Now list out equal angles from these triangles

4cm

4cm

5cm

7cm

4cm

5cm

7cm

A B

C P

Q

R

Thus we can write our earlier observation in more detail:

If the sides of a triangle are equal to the sides of another triangle, then the angle opposite to the equal sides of these triangles are equal

(1) Find all pair of matching angle

A B

C

3cm

4cm

5cm

3cm

5cm 4cm

PQ

R

BBBBBBBB

(2) Identify equal triangles from the given set of triangles

(3) In the quadrilateral ABCD shown below, AB=AD and BC=CD

A

B

C

D

Whether the triangle ABC and ADC are equal?

6

60◦

5cm

3cm

5cm

3cm

60◦

i

ii

3cm 3cm

4cm

70◦

4cm

CC

(4) ABC is a triangle and AC=CB, <B =40◦. Find the other two angles?

A

B C

If the angles of a triangle are equal to the angles of another triangle , would their sides are also be equal?

If the angles of a triangle are equal to the angles of another triangle ,would their sides are also be equal?

Two sides and an angle

Make cut outs of the triangles having length two sides and 6cm :and they meet an angle of 50◽

Put one triangle and place it in different positions over the other . And looking on third side.Change the side and angle and check

Given two distinct points A and Bin the plane, how manYydistinct points C are there onthe same plane such that ABC is an equilateral triangle?

‘ and

Let’s write our observations as a general principle

If two sides of a triangle and the angle made by them are equal to two sides of another triangle and the angle made by them, then the third sides of the triangle are also equal; the other two angles are also equal

By looking these triangle given

A

B

C

P

Q

R

Determining a triangle Bend a long piece of eerkiil to make an angle:

We want to make Triangle,placing another piece of eerkil Over the sides of this angle

Suppose we mark a spot On the upperside ofthe angle and Insist that the second eerkilmust pass through this

Now lets spot mark on upper and lower sides and eerkil to pass through both these spot

3

Why is that even though two sides and an angle are equal,the third sides are not equal?

1 Find all pair of matching angles

40 55

3cmA B

C

5cm

PQ

3cm

5cm

55◦

 

i)

ii)

60

X

YZL

MO

5cm

7cm

60◦

60◦

7cm

5cm

2) In the figure below M is the mid point of the line AB. Compute the other two angles of the triangle?

M

50◦

A B

C

3) In the figure below ,AC and BE are parallel lines:

AB D

EC

6cm

6cm

4cm 4cm

i) Are the lenghts of BC and DE equal? Why? ii) Are BC and DE parallel ? Why?

One side and two angles

If all sides of a triangle are specified , we can draw it; if two sides and angle made by them are specified, then also we can draw the triangle.What if the length of one side and the angles at the both of its end are specified?It can be drawn like this:

8cm

40◦ 60◦

Changing the positions of the angles, we can draw like this :

60◦ 40◦

8cm

It can be drawn in other ways too. Try outI9n all such triangle,what about the other two sides?

Cut out one side of these triangles and try to make coincide with others. The other two sides are also equal, right?

So we have a third general principle:

If one side of a triangle and angles at its ends are equal to one side of another triangle and the angles at its end, then the r=third angles are also equal.

In any triangle , the sum of all three angles is 180◦.so, if we know two angles of a triangle, then we can calculate the third.

Draw two triangles:

8cm

8cm

40◦ 6o◦

40◦ 80◦

What is the third angle of each triangle?

40◦ 6o◦

8cm40◦ 80◦

8cm

80◦

6o◦

Why is it that, even though one side and all angles are equal, the other two sides are not equal?

In any parallelogram, opposite sides are equal

In any parallelogram, the diagonals bisect each other

A B

CD

PARALLELOGRAM

AA

Looking backLearning outcomes

What I can

What teacher’s help

Must improve

To identify the triangleExplaining the various cases in which the equality of some measures of triangle imply the equality of other measures

Forming some principles from such principles about triangles.