Find Sides of Two Similar Triangles
Find Sides of Two Similar Triangles

Congruent  Triangles

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

If two triangles are equal in all respects, they are said to be
Congruent triangles.
Thus two congruent-triangles have the same shape and same size.

Let ΔABC and ΔPQR be two triangles. Then we can superimpose ΔABC on ΔPQR, so as to cover exactly.

Due to this superimposition :
Vertex A falls on Vertex P
Vertex B falls on Vertex Q
Vertex C falls on Vertex R
AB = PQ ∠A = ∠P
BC =QR ∠B = ∠Q
AC = PR ∠C = ∠R
Hence triangles ABC and PQR are congruent to each other.

Note : 1) Congruent-triangles are similar but the similar triangles are not always congruent.
2) The symbol reads " is congruent to ".

If two triangles are congruent then there is one to one correspondence (↔) between the two triangles.

ΔABC ↔ ΔPQR then

∠A ≅ ∠P , ∠B ≅ ∠Q and ∠C ≅ ∠R

∠AB ≅ ∠PQ , ∠BC ≅ ∠QR and ∠AC ≅ ∠PR .

Note : If two triangles are congruent then their corresponding parts are congruent.

Corresponding Parts of Congruent Triangles are Congruent
⇒ C. P .C. T. C

Congruence Relation

1) Every triangle is congruent to itself. ΔABC ≅ ΔABC.
2) If ΔABC ≅ ΔPQR then ΔPQR = ΔABC.
3) If ΔABC ≅ ΔPQR and ΔABC ≅ ΔDEF then ΔPQR ≅ ΔDEF.

Examples :

In the following pairs of triangles, find out whether the triangles in each pair are congruent or not.
1) ΔABC : AB = 3 , BC = 4 and ∠B = 900
ΔDEF : DE = 3 , DF = 4 and ∠E = 900.

Solution :
Here , ΔABC not ≅ Δ DEF because there is no one to one correspondence between BC and DF.

2) Δ ABC : AB = 3 , AC = 5 and BC = 6
Δ PQR : PQ = 3 , PR = 5 and QR = 6

Solution :
Here ΔABC ΔPQR because there is one to one correspondence between all the sides.


Introduction to Triangles
Types of Triangles on the basis of Sides
Types of Triangles on the basis of Angles
Angle Sum Property of Triangles
Exterior and Interior angles of Triangle
Triangle Inequality Property
Congruent Triangles
Postulates of Congruent Triangle
Inequality in Triangle


7th grade math

Home Page