Question

kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures.

Answer 1

If we have a kite ABCD where AB = CD and DC = CA.
Let E be a midpoint between BC
Since triangle ABC is an isosceles triangle, ray BE bisects angle ABC and is perpendicular to AC.
So, angle ABE = CBE.
Since also triangle CDA is isosceles, line DE is perpendicular to AC for the same reason. Therefore, AC is perpendicular to BD.