Q. 1345.0( 3 Votes )

In each of the given pairs of triangles of Fig. 6.42, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.






Answer :

Formula Used/Theory:-


ASA congruence criterion is in which 2 angles and a side between them are equal in both the triangles


(a) A = Q


But B≠P


Δ ABC and Δ PQR are not congruent


Result:- Δ ABC and Δ PQR are not congruent


(b) ABD = BDC


ADB = DBC


BD = BD (common in both triangle)


Δ ADB and Δ CBD are congruent by ASA


∆ADB ∆CBD


Result:- Δ ADB and Δ CBD are congruent by ASA


(c) ASA congruence criterion is in which 2 angles and a side between them are equal in both the triangles


X = L


Y = M


XY = ML


Δ XYZ and Δ LMN are congruent by ASA


∆XYZ ∆LMN


Result:- Δ XYZ and Δ LMN are congruent by ASA


(d) Angle sum property


Sum of all angles of triangle is 180°


By angle sum property


A + B + C = 180° D + E + F = 180°


Equating both


We get;


A + B + C = D + E + F


As B = F


A = D


Cancelling out we get, C = E


C = E


B = F


BC = FE


Δ ABC and Δ DFE are congruent by ASA


∆ABC ∆DFE


Result:- Δ ABC and Δ DFE are congruent by ASA


(e) In Δ PNO and Δ MNO


PNO = MON


MNO≠PON


ON = ON (common in both triangles)


Δ MNO and ΔPON are not congruent by ASA


Result:- Δ MNO and ΔPON are not congruent by ASA


(f) D = C


AOD = COB


OD = CO


Δ ADO and Δ BCO are congruent by ASA


∆ADO ∆BCO


Result:- Δ ADO and Δ BCO are congruent by ASA


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