Question

1. given: $overline{rv} cong overline{tk}$, and $overline{rv} parallel overline{tk}$,

prove: $\triangle rvk cong \triangle tkv$

statements \t\t\t\t\t\t\treasons
\t\t\t\t\t\t\t\tgiven
\t\t\t\t\t\t\t\tgiven
\t\t\t\t\t\t\t\t
\t\t\t\t\t\t\t\t
$\triangle rvk cong \triangle tkv$

Explanation:

Step1: Escribir dato 1

$\overline{RV} \cong \overline{TK}$

Step2: Escribir dato 2

$\overline{RV} \parallel \overline{TK}$

Step3: Ángulos alternos internos

$\angle RVK \cong \angle TKV$

Step4: Lado común

$\overline{VK} \cong \overline{VK}$

Step5: Congruencia SAS

$\triangle RVK \cong \triangle TKV$

Answer:

Statements	Reasons
$\overline{RV} \parallel \overline{TK}$	Given
$\angle RVK \cong \angle TKV$	Alternate interior angles theorem
$\overline{VK} \cong \overline{VK}$	Reflexive property of congruence
$\triangle RVK \cong \triangle TKV$	SAS Congruence Postulate