ABOUT EQAUL TRIANGLES IN A SIMPLE MANNER

2. ‫ههههه‬The sides are 3cn
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
5cm
3cm
5cm
or
Now draw with the 5centimetres Base:
5cm
3cm
3cm
5cm
or

3. 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.

4. n
Look at these triangles and
Now list out equal angles from these triangles
4cm
5cm
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
3cm
4cm
PQ
R

5. 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◦
3cm
60◦
i
ii
3cm 3cm
4cm
70◦

6. 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?

7. ‘ 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 thi
s angle
Suppose we mark a spot On the
upperside ofthe angle and
Insist that the second eerkil
must pass through this
Now lets spot mark on upper
and lower sides and eerkil to
pass through both these spot

8. 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
55
3cmA
B
C
P
Q
i)
ii)
60
X
YZ
L
MO
7cm
7cm

9. 2) In the figure below M is the mid point of the line AB. Compute
the other two angles of the triangle?
MA B
C
3) In the figure below ,AC and BE are parallel lines:
A B D
EC
4cm 4cm
i) Are the lenghts of BC and DE equal? Why?
ii) Are BC and DE parallel ? Why?

10. 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
Changing the positions of the angles, we can draw like this :
8cm
It can be drawn in other ways too. Try out
I9n 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?

11. 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
6o◦
40◦
80◦
What is the third angle of each triangle?
6o◦
8cm
40◦ 80◦
8cm
80◦
6o◦

12. 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

13. AA
Looking back
Learning
outcomes
What I
can
What
teacher’s
help
Must
improve
To identify the
triangle
Explaining 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.