Question

determine the missing reasons in the proof. statement reason abdc is a kite. given cd ≅ bd and ac ≅ ab definition of a kite ad ≅ ad reflexive property of congruence △cda ≅ △bda ∠cda ≅ ∠bda ed ≅ ed △ced ≅ △bed ce ≅ be ad bisects bc definition of a bisector sas criterion sss criterion asa criterion hl theorem

Explanation:

Step1: Recall triangle - congruence criteria

We have three pairs of corresponding sides equal: $\overline{CD}\cong\overline{BD}$, $\overline{AC}\cong\overline{AB}$, and $\overline{AD}\cong\overline{AD}$.

Step2: Identify the congruence criterion

Since all three pairs of corresponding sides of $\triangle CDA$ and $\triangle BDA$ are congruent, we use the SSS (Side - Side - Side) criterion for triangle congruence.

Step3: For $\angle CDA\cong\angle BDA$

Corresponding parts of congruent triangles are congruent (CPCTC). Since $\triangle CDA\cong\triangle BDA$, their corresponding angles are congruent.

Step4: For $\triangle CED\cong\triangle BED$

We have $\overline{CD}\cong\overline{BD}$, $\angle CDA\cong\angle BDA$, and $\overline{ED}\cong\overline{ED}$. So, by the SAS (Side - Angle - Side) criterion, $\triangle CED\cong\triangle BED$.

Step5: For $\overline{CE}\cong\overline{BE}$

By CPCTC, since $\triangle CED\cong\triangle BED$, their corresponding sides are congruent.

Answer:

For $\triangle CDA\cong\triangle BDA$: SSS criterion
For $\angle CDA\cong\angle BDA$: CPCTC
For $\triangle CED\cong\triangle BED$: SAS criterion
For $\overline{CE}\cong\overline{BE}$: CPCTC