Problem
GEO-B2-M09-P006 Diagonals of an Isosceles Trapezoid
#6
★★☆☆☆ Level 2 of 5
In an isosceles trapezoid, choose coordinates \(A(-a,0)\), \(B(a,0)\), \(D(-b,h)\), \(C(b,h)\), where \(a>b>0\), \(h>0\). Prove that \(AC=BD\).
Compare the squared lengths of the diagonals.
\(AC^2=(a+b)^2+h^2\). Also \(BD^2=(-a-b)^2+h^2=(a+b)^2+h^2\). Therefore \(AC=BD\).
Shows how symmetric coordinates remove unnecessary algebra.