In triangles $ABC$ and $DEF$,$\angle A = \angle D$,$\angle B = \angle E$ and $AB = EF$. Will the two triangles be congruent? Give reasons for your answer.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(NO) The two triangles are not necessarily congruent. For two triangles to be congruent by the $ASA$ (Angle-Side-Angle) criterion,the side must be included between the two angles. In $\triangle ABC$,the side included between $\angle A$ and $\angle B$ is $AB$. In $\triangle DEF$,the side included between $\angle D$ and $\angle E$ is $DE$. Since the given condition is $AB = EF$ instead of $AB = DE$,the triangles do not satisfy the $ASA$ congruence criterion. Therefore,they are not necessarily congruent.

Explore More

Similar Questions

For any convex quadrilateral $ABCD$,prove that $AB + BC + CD + DA > AC + BD$.

$ABC$ is a right triangle such that $AB = AC$ and the bisector of angle $C$ intersects the side $AB$ at $D$. Prove that $AC + AD = BC$.

Difficult
View Solution

State whether the following statement is true or false:
$(1)$ $\angle ABD$ and $\angle ACE$ are the exterior angles of $\Delta ABC$. If $\angle ABD = 110^{\circ}$ and $\angle ACE = 130^{\circ}$,then $AB > AC$.

In $\Delta PQR$,$\angle Q = \angle R$ and $PQ = 6.5 \, cm$,then find $PR$. (in $, cm$)

If in $\Delta ABC, AC > AB > BC$,then find the greatest angle of the triangle.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo