Question

given: quadrilateral abcd is a kite.
prove: \\( \triangle aed \cong \triangle ced \\)
it is given that quadrilateral abcd is a kite. we know that \\( \overline{ad} \cong \overline{cd} \\) by the definition of. by the kite diagonal theorem, \\( \overline{ac} \\) is to \\( \overline{bd} \\). this means that angles aed and ced are right angles. we also see that \\( \overline{ed} \cong \overline{ed} \\) by the property. therefore, we have that \\( \triangle aed \cong \triangle ced \\) by.

Explanation:

• A kite has two distinct pairs of adjacent sides that are equal. So, \(\overline{AD}\cong\overline{CD}\) by the definition of a kite.
• The kite diagonal theorem states that one diagonal of a kite is perpendicular to the other diagonal. So, \(\overline{AC}\) is perpendicular to \(\overline{BD}\).
• \(\overline{ED}\cong\overline{ED}\) by the reflexive property (a segment is congruent to itself).
• For right - angled triangles \(\triangle AED\) and \(\triangle CED\), we have \(\overline{AD}\cong\overline{CD}\) (hypotenuse), \(\overline{ED}\cong\overline{ED}\) (common leg). By the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles, \(\triangle AED\cong\triangle CED\).

Answer:

1. kite
2. perpendicular
3. reflexive
4. HL (Hypotenuse - Leg)