Question

Select the correct answer from each drop-down menu. given: kite with diagonals and intersecting at e. prove: bisects a diagram of a kite abcd. a horizontal and a vertical line connect ad and cb. the lines ad and cb intersect at e. determine the missing reasons in the proof. statement reason is a kite. given and definition of a kite reflexive property of congruence cpctc reflexive property of congruence cpctc bisects definition of a bisector

Answer 1

The reasons are

• ΔCDA ≅ ΔBDA by SSS
• ΔCED ≅ ΔBED by SAS

How to get the reasons

ABCD is a kite, with its diagonals AD and BC.

Given:

AC = AB

CD = BD (Property of Kite)

In triangles ACD and ABD:

AC = AB

CD = BD (Property of Kite)

AD = AD (Common side)

Using the SSS (Side Side Side) Criteria:

ΔACD ≅ ΔABD

Therefore, ∠CDA = ∠BDA (CPCT - Corresponding Parts of Congruent Triangles)

Now, in triangles CDE and BDA:

CD = BD

∠CDE = ∠BDE

DE = DE (Common side)

By the SAS (Side Angle Side) Criteria:

ΔCDE ≅ ΔBDA

Hence, CE = BE (CPCT - Corresponding Parts of Congruent Triangles)

This demonstrates that AD bisects BC into equal parts.