Question

Prove that the base angles of an isosceles trapezium are congurent.

Answer 1

R.E.F image

Base angles of isosceles trapezoid are congurent

Draw 2 lens to base $\overline{BE}$ & $\overline{CF}$

$\overline{BF}\cong \overline{CF}$ $[\because$ they are altitudes]

$\overline{AB}\cong \overline{CD}$ [Given]

$\overline{AE}\cong \overline{FD}$ [By hypotenuse]

$\Delta ABC\cong \Delta DCF$ $[\because$ sss congurency]

$\therefore \angle A\cong \angle D$ since corresponding parts of congurent

triangles are congurent.