Question

Given: Quadrilateral ABCD is a kite. Prove: ΔAED ≅ ΔCED Kite A B C D is shown. Diagonals are drawn from point A to point C and from point B to point D and intersect at point E. It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see that ED ≅ ED by the property. Therefore, we have that ΔAED ≅ ΔCED by .

Answer 1

Answer:

1. kite 2. perpendiclular 3. reflective 4. HL

Step-by-step explanation:

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Answer 2

Answer:

We know that AD ≅ CD by the definition of kite. By the kite diagonal theorem, AC is perpendicular to BD. This means that angles AED and CED are right angles. We also see that ED ≅ ED by the reflexive property. Therefore, we have that ΔAED ≅ ΔCED by HL.

Step-by-step explanation:

We know that AD ≅ CD by the definition of kite.

- adjacent sides in a kite are congruent

By the kite diagonal theorem, AC is perpendicular to BD.

- the kite diagonal theorem states that diagonals of a kite form right angles because they are perpendicular to each other.

We also see that ED ≅ ED by the reflexive property.

- any side or angle congruent to itself is identified by the reflexive property

Therefore, we have that ΔAED ≅ ΔCED by HL.

- the triangles formed are all right triangles, so we can they that the two triangles are congruent to each other by the Hypotenuse Leg theorem.