![\"\"](\"/userfiles/image/steps_images/step1.JPG\")
If the legs of the trapezoid are congruent, then the trapezoid is isosceles trapezoid.
\Use the Distance Formula to determine whether the legs are congruent.
\The distance formula is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=3e20b893d28147dadc2960b44d6dc0a6.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=ae439fc169d10b66f7459cdb65a46102.png\")
(Substitute ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=0f8033571e69a0454bb576d9151f588d.png\")
)
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=5d8a4212d38b6d25354450f3fc6895fe.png\")
(Simplify)
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=34e480b675a2e653d4b3149b1e34ecf7.png\")
(Substitute ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=8a84b84d66023d52a67960399e8a0ce4.png\")
)
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=fe23a8904e6cfdd443cd419394ea550f.png\")
(Simplify)
Since the legs are not congruent, QRST is not an isosceles trapezoid.![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
The trapezoid QRST is not an isosceles trapezoid.