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Isosceles trapezoid LMNP with LN congruent to PN, and diagonals LN and PM
Show LN = PM
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Your formulation is FAR from perfect.
More accurate statement is this.
Diagonals of an isosceles trapezoid are congruent.
For the proof see the lesson
-Diagonals of an isosceles trapezoid are congruent
in this site.
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lesson is the part if this textbook under the topic "Properties of polygons".