On one stage, a 1,000-gallon swimming pool stands in for Iran as it’s about to suffer a Western-backed coup. On the other, Blake Hackler performs 35 to 40 roles, centrally a German transgender antiquarian who survived the Nazi and Soviet regimes. Based on true stories, they prove that plays can present history imaginatively.

Produced by Amphibian Stage, “Ajax” is billed as a noir comedy set in a North Tehran villa where an American CIA operative (Carson Wright) puts in motion the overthrow of the country’s first democratically elected prime minister and the reinstallation of the Shah (David Mattar Merten). The pool is given voice by an actor (Jovane Caamaño).

Playwright Habib Yazdi’s satirical approach to the events of August 1953 that followed the prime minister’s nationalization of the British-owned oil industry includes telling the story from the point of view of the villa’s pool boy (Shayan Hooshmand), who strikes up a friendship with the American spy.

“The pool isn’t just scenery, it’s a character and a witness,” says scenic designer Leah Mazur. “It is present for the history unfolding around it, responding to everybody who enters it and every disturbance of its surface.”

Meanwhile, Theatre Three’s production of Dallas native Doug Wright’s Pulitzer and Tony winning solo show “I Am My Own Wife” follows the harrowing adventures of Charlotte von Mahlsdorf, a transgender woman who successfully navigated some of the most turbulent chapters in German history — sometimes by accommodating the authorities — while preserving a collection of the country’s antiquities.

Hackler, theater chair at Southern Methodist University and resident actor at Dallas Theater Center, portrays von Mahlsdorf and a host of other characters, including government officials, reporters and family members. Wright, who got his start acting at Theatre Three, interviewed her as part of his research.

“First and foremost, it’s just a great piece of theater, especially when performed by such an accomplished actor as Blake Hackler,” says Theatre Three artistic director Jeffrey Schmidt. “Add to that a director like Garret Storms whose attention to detail and refined storytelling are unmatched and you have a thrilling night of live performance.”

“I Am My Own Wife” through Nov. 1 at 2688 Laclede St., Dallas. $37-$40. theatre3dallas.com.