Question

given: abcd is a trapezoid.$overline{ba} cong overline{cd}$prove: $overline{bd} cong overline{ca}$angles segments triangles statements reasonssascpctcgivenreflexive propertystatements1. $overline{ba} cong overline{cd}$2. abcd is a trapezoid3. abcd is an isosceles trapezoid4. $overline{ad} cong overline{ad}$5. $angle bad cong angle cda$reasons1. given2. given3. def. of isosceles trapezoid4. reflexive property5. base angles theoremcorrect! assemble the next statement.

Explanation:

Step1: State triangle congruence

$\triangle BAD \cong \triangle CDA$

Step2: Justify with SAS rule

Reason: SAS

Step3: Derive final segment congruence

$\overline{BD} \cong \overline{CA}$ (by CPCTC)

Answer:

Next Statement & Reason:

1. $\boldsymbol{\triangle BAD \cong \triangle CDA}$
2. $\boldsymbol{SAS}$

Final Completed Proof Step:

1. $\boldsymbol{\overline{BD} \cong \overline{CA}}$
2. $\boldsymbol{CPCTC}$