Question

Write the names of congruent triangles with proper correspondence in the vertices.

(i) In $∆$XYZ and DYZ, seg XZ $\cong$ seg DY, $\angle$XZY $\cong$ $\angle$ZYD
(ii) In $∆$EFG and $∆$LMN, seg FG $\cong$ seg MN, $\angle$G $\cong$ $\angle$N, $\angle$F $\cong$ $\angle$M
(iii) In $∆$MNO and $∆$CNR, $\angle$MNO $\cong$ $\angle$CNR, seg MN $\cong$ seg CN, seg NO $\cong$ seg NR
(iv) In $∆$BTR and $∆$BTP, seg BR $\cong$ seg BP, seg RT $\cong$ seg TP
(v) In $∆$LMP and $∆$LPN, $\angle$LMP $\cong$ $\angle$LNP, LPM $\cong$ $\angle$NPL

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{seg}\mathrm{XZ}\cong \mathrm{seg}\mathrm{YD}\left(g\mathrm{iven}\right) \\ \angle \mathrm{XZY}\cong \angle \mathrm{DYZ},\left(g\mathrm{iven}\right) \\ \mathrm{seg}\mathrm{YZ}\cong \mathrm{seg}\mathrm{YZ}\left(\mathrm{common}\right) \\ \therefore △\mathrm{XYZ}\cong △\mathrm{DZY}(by\mathrm{SAS}\mathrm{congruency}\mathrm{test}) \end{gathered}$$


$$\begin{gathered} \left(\mathrm{ii}\right)\angle \mathrm{F}\cong \angle \mathrm{M}\left(g\mathrm{iven}\right) \\ \mathrm{seg}\mathrm{FG}\cong \mathrm{seg}\mathrm{MN}\left(g\mathrm{iven}\right) \\ \angle \mathrm{G}\cong \angle \mathrm{N}\left(g\mathrm{iven}\right) \\ \therefore △\mathrm{EFG}\cong △\mathrm{LMN}(by\mathrm{ASA}\mathrm{congruency}\mathrm{test}) \end{gathered}$$



$$\begin{gathered} \left(\mathrm{iii}\right)\mathrm{seg}\mathrm{CN}\cong \mathrm{seg}\mathrm{MN}\left(g\mathrm{iven}\right) \\ \mathrm{seg}\mathrm{RN}\cong \mathrm{seg}\mathrm{NO}\left(g\mathrm{iven}\right) \\ \angle \mathrm{CNR}\cong \angle \mathrm{MNO}\left(g\mathrm{iven}\right) \\ \therefore △\mathrm{CNR}\hspace{0.17em}\cong △\mathrm{MNO}(by\mathrm{SAS}\mathrm{congruency}\mathrm{test}) \end{gathered}$$



$$\begin{gathered} \left(\mathrm{iv}\right)\mathrm{seg}\mathrm{BR}\cong \mathrm{seg}\mathrm{BP}\left(g\mathrm{iven}\right) \\ \mathrm{seg}\mathrm{RT}\cong \mathrm{seg}\mathrm{PT}\left(g\mathrm{iven}\right) \\ \mathrm{seg}\mathrm{BT}\cong \mathrm{seg}\mathrm{BT}\left(\mathrm{common}\right) \\ \therefore △\mathrm{BRT}\cong △\mathrm{BPT}(by\mathrm{SSS}\mathrm{congruency}\mathrm{test}) \end{gathered}$$



$$\begin{gathered} \left(\mathrm{v}\right)\angle \mathrm{LMP}\cong \angle \mathrm{LNP} \\ \angle \mathrm{MPL}\cong \angle \mathrm{NPL} \\ \mathrm{seg}\mathrm{LP}\cong \mathrm{seg}\mathrm{PL}\left(\mathrm{common}\right) \\ \therefore △\mathrm{LMP}\cong △\mathrm{LNP}(\mathrm{AAS}\mathrm{test}) \end{gathered}$$