In $\Delta ABC$ and $\Delta DEF$,$AB = DE$,$AB \parallel DE$,$BC = EF$ and $BC \parallel EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that quadrilateral $ABED$ is a parallelogram.
(N/A) To prove that $ABED$ is a parallelogram.
We know that a quadrilateral is a parallelogram if a pair of opposite sides is parallel and equal in length.
Given:
$AB = DE$
$AB \parallel DE$
In quadrilateral $ABED$,we have a pair of opposite sides ($AB$ and $DE$) which are both parallel and equal in length.
Therefore,$ABED$ is a parallelogram.
We know that a quadrilateral is a parallelogram if a pair of opposite sides is parallel and equal in length.
Given:
$AB = DE$
$AB \parallel DE$
In quadrilateral $ABED$,we have a pair of opposite sides ($AB$ and $DE$) which are both parallel and equal in length.
Therefore,$ABED$ is a parallelogram.
Explore More
Similar Questions
In $\Delta ABC$ and $\Delta DEF$,$AB = DE$,$AB \parallel DE$,$BC = EF$ and $BC \parallel EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively (see Fig). Show that $\Delta ABC \cong \Delta DEF$.
Medium
View SolutionShow that if the diagonals of a quadrilateral are equal and bisect each other at right angles,then it is a square.
Difficult
View SolutionIn a parallelogram $ABCD$,$E$ and $F$ are the mid-points of sides $AB$ and $CD$ respectively (see Fig). Show that the line segments $AF$ and $EC$ trisect the diagonal $BD$.
Difficult
View Solution$ABCD$ is a trapezium in which $AB \parallel CD$ and $AD = BC$ (see Fig). Show that $\angle C = \angle D$.
Medium
View Solution$ABCD$ is a rectangle in which diagonal $AC$ bisects $\angle A$ as well as $\angle C$. Show that $ABCD$ is a square.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo