4. Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by ASA congruence rule. In the case of congruence, write it in symbolic form.

                             \bigtriangleup DEF                                                                                                 \bigtriangleup PQR

        (i)\angle D= 60^{o},\angle F= 80^{o},DF= 5cm                                            \angle Q= 60^{o},\angle R= 80^{o},QR= 5cm
       (ii)\angle D= 60^{o},\angle F= 80^{o},DF= 6cm                                            \angle Q= 60^{o},\angle R= 80^{o},QP= 6cm
       (iii)\angle D= 80^{o},\angle F= 30^{o},EF= 5cm                                           \angle P= 80^{o},PQ= 5 cm,\angle R= 30^{o}

         

Answers (2)

i)

Given in \bigtriangleup DEF and  \bigtriangleup PQR.

\\\angle D=\angle Q= 60^{o}\\\angle F=\angle R= 80^{o}\\DF=QR= 5cm

So, by ASA congruency criterion, they are congruent to each other.i.e.

\bigtriangleup DEF\cong\Delta QPR.

ii)

Given in \bigtriangleup DEF and  \bigtriangleup PQR.

\\\angle D=\angle Q= 60^{o}\\\angle F=\angle R= 80^{o}\\DF=QP= 6cm

For congruency by ASA criterion, we need to be sure of equity of the side which is joining the two angles which are equal to their corresponding parts. Here the side QR is not given which is why we cannot conclude the congruency of both the triangles.

iii)

Given in \bigtriangleup DEF and  \bigtriangleup PQR.

\\\angle D=\angle Q= 60^{o}\\\angle F=\angle R= 80^{o}\\DF=QP= 6cm

For congruency by ASA criterion, we need to be sure of equity of the side which is joining the two angles which are equal to their corresponding parts. Here the side QR is not given which is why we cannot conclude the congruency of both the triangles.

 

Given in \bigtriangleup DEF and \bigtriangleup PQR.

 

\\\angle D=\angle Q= 60^{o}\\\angle F=\angle R= 80^{o}\\DF=QR= 5cm

 

So, by ASA congruency criterion, they are congruent to each other.i.e.

 

\bigtriangleup DEF\cong\Delta QPR.

 

ii)

 

Given in \bigtriangleup DEF and \bigtriangleup PQR.

 

\\\angle D=\angle Q= 60^{o}\\\angle F=\angle R= 80^{o}\\DF=QP= 6cm

 

For congruency by ASA criterion, we need to be sure of equity of the side which is joining the two angles which are equal to their corresponding parts. Here the side QR is not given which is why we cannot conclude the congruency of both the triangles.

 

iii)

 

Given in \bigtriangleup DEF and \bigtriangleup PQR.

 

\\\angle D=\angle Q= 60^{o}\\\angle F=\angle R= 80^{o}\\DF=QP= 6cm

 

For congruency by ASA criterion, we need to be sure of equity of the side which is joining the two angles which are equal to their corresponding parts. Here the side QR is not given which is why we cannot conclude the congruency of both the triangles.

 

 

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