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Draw another DXYZ, with YZ = 4 cm, ∠Y = 60º, ∠Z = 40º, such that BC = YZ, ∠B = ∠Y, ∠C = ∠Z.

Make a trace copy of DABC and try to cover DXYZ with A on X, B on Y and C on Z.
We observe that, the two triangles cover each other exactly. Therefore, DABC ≅ DXYZ.

AAS Congruence Criterion (Angle-Angle-Side)

Two triangles have two equal angles and a side adjacent to only A P
one of the angles are equal, then two triangles are congruent.
Draw DABC and DPQR, where BC = QR, ∠A = ∠P and ∠B = ∠Q.

We observed that both the triangles are superimposed on each B C Q R
other. Therefore, DABC ≅ DPQR.

RHS Congruence Criterion (Right Angle – Hypotenuse – Side)

Two right triangles are congruent if the hypotenuse and one side of the first triangle are
respectively equal to the hypotenuse and one side of the other triangle.

Draw a DABC with ∠B = 90°, BC = 4 cm and hypotenuse AC = 5 cm.
Draw another DDEF, right angled at E with hypotenuse DF = 5 cm and side EF = 4 cm.

Remember
Two congruent figures are equal in
area. But the converse is not true.
As there can be two figures which
are equal in area and yet, they may
Now make a trace copy of DDEF and place it on DABC. not be congruent.
You will observe that DDEF covers DABC exactly.

Therefore, DABC ≅ DDEF. A
Example 19: In the given figure, AD = CD and AB = CB.

(a) State the three pairs of equal parts in DABD and DCBD.

(b) Is DABD ≅ DCBD? Why or why not?
C
(c) Does BD bisect ∠ABC? Give reasons.

Solution:
If three angles of a triangle are
(a) In DABD and DCBD, equal to three angles of the
Note:
AB = CB (Given) other triangle, then the triangles
are not necessarily congruent.
AD = CD (Given)

and BD = BD (Common side to both triangles)

(b) From part (a) above, DABD ≅ DCBD (By SSS congruence criterion)
(c) ∠ABD = ∠CBD (C.P.C.T.)

(C.P.C.T. is corresponding parts of congruent triangles)
Hence, BD bisects ∠ABC.

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