Question

State the correspondence between the vertices, sides and angles of the following pairs of congruent triangles.

(i) ∆ABC ≅ ∆EFD
(ii) ∆CAB ≅ ∆QRP
(iii) ∆XZY ≅ ∆QPR
(iv) ∆MPN ≅ ∆SQR

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}\mathrm{to}\mathrm{state}\mathrm{the}\mathrm{correspondence}\mathrm{between}\mathrm{the}\mathrm{vertices},\mathrm{sides}\mathrm{and}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{pairs}\mathrm{of}\mathrm{congruent}\mathrm{triangles}. \\ \left(\mathrm{i}\right)△ABC\cong △EFD \\ \mathrm{Correspondence}\mathrm{between}\mathrm{vertices}: \\ A\leftrightarrow E,B\leftrightarrow F,C\leftrightarrow D \\ \mathrm{Correspondence}\mathrm{between}\mathrm{sides}: \\ AB=EF,BC=FD,CA=DE \\ \mathrm{Correspondence}\mathrm{between}\mathrm{angles}: \\ \angle A=\angle E,\angle B=\angle F,\angle C=\angle D \\ \left(\mathrm{ii}\right)△CAB\cong △QRP \\ \mathrm{Correspondence}\mathrm{between}\mathrm{vertices}: \\ C\leftrightarrow Q,A\leftrightarrow R,B\leftrightarrow P \\ \mathrm{Correspondence}\mathrm{between}\mathrm{sides}: \\ CA=QR,AB=RP,BC=PQ \\ \mathrm{Correspondence}\mathrm{between}\mathrm{angles}: \\ \angle C=\angle Q,\angle A=\angle R,\angle B=\angle P \\ \left(\mathrm{iii}\right)△XZY\cong △QPR \\ \mathrm{Correspondence}\mathrm{between}\mathrm{vertices}: \\ X\leftrightarrow Q,Z\leftrightarrow P,Y\leftrightarrow R \\ \mathrm{Correspondence}\mathrm{between}\mathrm{sides}: \\ XZ=QP,ZY=PR,YX=RQ \\ \mathrm{Correspondence}\mathrm{between}\mathrm{angles}: \\ \angle X=\angle Q,\angle Z=\angle P,\angle Y=\angle R \\ \left(\mathrm{iv}\right)△MPN\cong △SQR \\ \mathrm{Correspondence}\mathrm{between}\mathrm{vertices}: \\ M\leftrightarrow S,P\leftrightarrow Q,N\leftrightarrow R \\ \mathrm{Correspondence}\mathrm{between}\mathrm{sides}: \\ MP=SQ,PN=QR,NM=RS \\ \mathrm{Correspondence}\mathrm{between}\mathrm{angles}: \\ \angle M=\angle S,\angle P=\angle Q,\angle N=\angle R \end{gathered}$$