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If two triangles are equal in all respects, they are said to beThus 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.

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.

2) The symbol

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

∠A ≅ ∠P , ∠B ≅ ∠Q and ∠C ≅ ∠R

∠AB ≅ ∠PQ , ∠BC ≅ ∠QR and ∠AC ≅ ∠PR .

⇒ C. P .C. T. C

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.

1) ΔABC : AB = 3 , BC = 4 and ∠B = 90

ΔDEF : DE = 3 , DF = 4 and ∠E = 90

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

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

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