3. In Fig 7.27, measures of some parts are indicated. By applying ASA congruence rule, state which pairs triangles are congruent. In case of congruence, write the result in symoblic form.

             

            

Answers (1)

i) in \Delta ABC and \Delta FED

AB = FE = 3.5 cm 

\angle A = \angle F = 40 ^0

\angle B = \angle E = 60^0

So by ASA congruency rule, both triangles are congruent.i.e.

\Delta ABC \cong \Delta FED

ii) in \Delta PQR and \Delta FDE

\angle Q= \angle D= 90 ^0

\angle R= \angle E = 50^0

But,

\overline {EF}\neq\overline {RP}

So, given triangles are not congruent.

iii) in \Delta RPQ and \Delta LMN

RQ = LN = 6 cm 

\angle R = \angle L = 60 ^0

\angle Q= \angle N= 30^0

So by ASA congruency rule, both triangles are congruent.i.e.

\Delta RPQ\cong \Delta LMN.

iv) in \Delta ADB and \Delta BCA

AB = BA (common side)

\angle CAB = \angle DBA= 30 ^0

\angle D= \angle C=180^0-30^0-30^0-45^0=75^0

So by ASA congruency rule, both triangles are congruent.i.e.

\Delta ADB \cong \Delta BCA

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