CK12 - Geometry

So, the two diagonalsin the isoscelestrapezoidare congruent.This will be true in any isoscelestrapezoids.

IdentifyingIsoscelesTrapezoidswith Diagonals

The conversestatementof the theoremstatingthat diagonalsin an isoscelestriangleare congruentis also
true. If a trapezoidhas congruentdiagonals,it is an isoscelestrapezoid.You can eitheruse measurements
shownon a diagramor use the distanceformulato find the lengths.If you can provethat the diagonalsare
congruent,then you can identifythe trapezoidas isosceles.

Theorem:If a trapezoidhas congruentdiagonals,then it is an isoscelestrapezoid

Example 4

Is the trapezoidon the followinggrid isosceles?

It is true that you couldfind the lengthsof the two sidesto identifywhetheror not this trapezoidis isosceles.
However, for the sakeof this lesson,comparethe lengthsof the diagonals.

Beginby findingthe lengthof. The coordinatesof are and the coordinatesof are
.

Now find the lengthof. The coordinatesof are (5,5) and the coordinatesof are (0,-1).