Criteria of congruency of triangles.

1. CONGRUENCY OF
TRIANGLES
BY: Dr. Vivek Naithani
T.G.T Mathematics (Kendriya Vidyalaya
Sangathan)
Copyright Information: CC by SA 4.0

2. TRIANGLE
•A triangle is a closed plane figure bounded by 3
line segments.
•It has 3 sides, 3 vertices and 3 interior angles.
•The sum of all the interior angles of a triangle is
180o .
•The exterior angle formed by extending any one
side of a triangle is equal to the sum of interior

3. CONGRUENCY
 Two figures which are equal in area and similar in
shape are said to be congruent figures.
If we overlap two congruent figures on each other
they completely cover each other.
e.g. : Two currency notes of same denomination,
Slices of bread from the same loaf, biscuits from
the same packet.
This property of congruent figures is called

4. CONGRUENT
TRIANGLES
•Two triangles are said to be congruent if they
are equal in areas and similar in shapes.
•The completely cover each other when they
are kept one over the other.
•When two triangles are congruent their all the
three sides are equal and their all the angles
are also equal.

5. Two triangles ABC and DEF are
congruent
When triangle DEF is overlapped on triangle ABC
When triangle ABC is overlapped on Triangle

6. CRITERIA OF CONGRUENCY OF
TRIANGLES
1. SIDE- SIDE- SIDE (S.S.S) :
If all the three sides of one triangle are equal
to the corresponding three sides of another
triangle then the triangles are congruent by
side- side - side (S.S.S) congruency.

7. Here in triangle ABC and triangle DEF
AB = DE
BC = EF
AC = DF
∆𝑨𝑩𝑪 ≅ ∆𝑫𝑬𝑭 { 𝑺. 𝑺. 𝑺}

8. 2. SIDE - ANGLE – SIDE
(S.A.S)
If two sides and the included angle of one triangle
are equal to the corresponding two sides and the
included angle of another triangle, then the
triangles are congruent by side – angle – side.
Here it is important that the angle considered for
congruency must lie between the equal sides.

10. 3. ANGLE-SIDE-ANGLE (A-S-A)
OR
ANGLE-ANGLE-SIDE (A-A-S)
• If two angles and one side of a triangle of a triangle are
equal to the corresponding two angles and the
corresponding side of another triangle then the triangles
are said to be congruent by A.S.A or A.A.S
• Note: When two angles of a triangle are equal to two
angles of the another triangle then the third angles will be
automatically equal as the sum of all the three interior
angles is 180o . Hence A.A.S and A.S..A can be considered

13. 4. RIGHT ANGLE- HYPOTENUSE-
SIDE (R.H.S)
If the hypotenuse and any one side of a right
angled triangle are equal to the corresponding
hypotenuse and the corresponding side of
another right angled triangle then the triangles
are congruent by R.H.S congruency.
This property is applicable only to right angled

15. THANK
YOU