Question

Given below are some measurements of some parts of two triangles. Examine whether the two triangles are congruentor not by ASA congruence rule. In case they are congruent write them in symbolic form.
1. <D=60 degree , <F =60 degree , DF=5cm
​angle Q=60 degree , angle R= 60 degree , QP=5cm
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Answer 1

$$\begin{gathered} \mathrm{Since}\mathrm{two}\mathrm{angle}\mathrm{of}\mathrm{both}\mathrm{the}\mathrm{triangle}\mathrm{is}60\mathrm{degree}\mathrm{and}\mathrm{hence}\mathrm{third}\mathrm{angle}\mathrm{of}\mathrm{each}\mathrm{triangle} \\ \mathrm{will}\mathrm{also}\mathrm{be}60\mathrm{degree}\mathrm{now}\mathrm{all}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{both}\mathrm{the}\mathrm{triangle}\mathrm{are}60\mathrm{degree} \\ \mathrm{and}\mathrm{also}\mathrm{side}\mathrm{of}\mathrm{a}\mathrm{equilateral}\mathrm{triangle}\mathrm{is}\mathrm{equal}\mathrm{and}\mathrm{here}\mathrm{both}\mathrm{the}\mathrm{triangle}\mathrm{has}\mathrm{side} \\ 5\mathrm{cm}\mathrm{so}\mathrm{basically}\mathrm{both}\mathrm{the}\mathrm{triangle}\mathrm{are}\mathrm{congruence}. \\ △\mathrm{DFE}\cong △\mathrm{QPR} \end{gathered}$$