Question

ID
3. Given below are measurements of some parts of
two triangles. Examine whether the two triangles
are congruent by ASA congruence rule. In case they
are congruent, write them in symbolic form.
(a) D = 60° ZF = 80° DF = 5 cm
ZQ = 60° ZR = 40° QP = 5 cm
231​

Answer 1

Answer:

Step-by-step explanation:

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.