Question

Isocelew Trapezium Base Angles Congruent Proof

Answer 1

Let ABCD be an isosceles trapezoid such that BC || AD and AB congruent to CD. To prove angle A is congruent to angle D Proof BE and CF altitudes are drawn on AD. BE congruent to CF, since they are altitudes of same trapezoid. In right triangles AEB and DFC => AB congruent to CD ( given) => BE congruent to CF ( from above ) => AE congruent to FD ( as in right triangles corresponding hypotenuse are equal and one of the corresponding leg is congruent , so other leg is congruent) So by SSS criterion, triangle ABE is congruent to triangle DFC. Thus, by CPCT angle A is congruent to angle D Hence proved