10th Class Mathematics Triangles Question Bank MCQs - Triangles

In two triangles ABC and DEF, \[\angle A=\angle E\] and \[\angle B=\angle F\]. Then, \[\frac{AB}{AC}\] is equal to:

A) \[\frac{DE}{DF}\]

B) \[\frac{ED}{EF}\]

C) \[\frac{EF}{ED}\]

D) \[\frac{EF}{DF}\]

Correct Answer: C

Solution :

[c] In \[\Delta ABC\]and \[\Delta EFD\].

\[\angle A=\angle E\]and \[\angle B=\angle F\] (Given)

\[\therefore \,\,\,\,\,\Delta ABC\tilde{\ }\Delta EFD\](By AA similarity criterion)

\[\therefore \,\,\,\,\frac{AB}{EF}=\frac{AC}{ED}\Rightarrow \frac{AB}{AC}=\frac{EF}{ED}\]