# 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.

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

BD = BD (common in both triangle)

Δ ADB and Δ CBD are congruent by ASA

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