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

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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.

$\Delta ADB \cong \Delta BCA$

Posted by

Pankaj Sanodiya

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