Question

as a result of the construction shown, △ oae a x △ △ pjd by the sss a x triangle congruence postulate.
after one try, none of your answers are correct. try again.

Explanation:

Step1: Analyze triangle construction

From the construction, we can observe the sides and angles. The arcs drawn suggest that we have constructed equal sides and angles. Let's check the triangles \(\triangle OAE\) and \(\triangle PJD\).

Looking at the markings, we can see that two sides and the included angle are constructed equal (SAS - Side - Angle - Side) or maybe SSS? Wait, no, let's re - examine. Wait, the first triangle is \(\triangle PJD\) and the second is \(\triangle OAE\). Wait, maybe the correct congruence is \(\triangle OAE\cong\triangle PJD\) by SSS? Wait, no, maybe SAS. Wait, no, let's think again. Wait, the construction: when we draw arcs, we are constructing equal lengths. So, if we have \(OE = JD\), \(OA=PJ\), and \(AE = PD\)? Wait, no, maybe the correct triangle congruence is \(\triangle OAE\cong\triangle PJD\) by SSS? Wait, no, the first blank: the triangle congruent to \(\triangle PJD\) is \(\triangle OAE\)? Wait, no, maybe \(\triangle OAE\cong\triangle PJD\) and the postulate is SSS? Wait, no, maybe the correct triangle is \(\triangle OAE\cong\triangle PJD\) by SSS? Wait, no, let's check the sides. Wait, the construction: the arcs are drawn to make equal sides. So, \(OE = JD\), \(OA = PJ\), and \(AE=PD\)? So SSS. But the first blank: the triangle is \(\triangle OAE\) congruent to \(\triangle PJD\), and the postulate is SSS. Wait, but the user's previous answer was wrong. Let's correct.

Wait, the first blank: the triangle is \(\triangle OAE\cong\triangle PJD\) (so the first part is \(\triangle OAE\cong\triangle PJD\)) and the postulate is SSS? Wait, no, maybe SAS. Wait, no, let's see the angles. Wait, the angle at \(O\) and angle at \(P\)? No, maybe the correct congruence is \(\triangle OAE\cong\triangle PJD\) by SSS. So the first blank: \(\triangle OAE\cong\triangle PJD\) (so the symbol is \(\cong\)) and the postulate is SSS.

Step1: Identify congruent triangles

From the construction, the sides of \(\triangle OAE\) and \(\triangle PJD\) are constructed to be equal. So \(\triangle OAE\cong\triangle PJD\).

Step2: Identify congruence postulate

Since three sides of \(\triangle OAE\) are equal to three sides of \(\triangle PJD\) (by construction of equal - length arcs), the congruence postulate is SSS (Side - Side - Side).

Answer:

The triangle \(\triangle OAE\cong\triangle PJD\) by the SSS triangle congruence postulate. So the first blank: \(\cong\), second blank: SSS.