Question

1. a triangle with exactly one line of reflectional symmetry
2. a circle with center at p, radii $overline{pa}$ and $overline{pt}$, and chord $overline{ta}$ creating a minor arc $widehat{ta}$

Explanation:

Step1: Recall triangle types

An isosceles triangle has exactly one line of reflectional symmetry. It can be folded along the line that bisects the angle between the two equal - length sides and also bisects the opposite side.

Step2: Recall circle elements

To draw a circle with center \(P\), use a compass to set the radius length equal to the length of \(\overline{PA}\) or \(\overline{PT}\). Then, mark two points \(A\) and \(T\) on the circle. The line segment \(\overline{TA}\) is the chord, and the shorter arc between \(T\) and \(A\) is the minor arc \(\widehat{TA}\).

Answer:

1. An isosceles triangle satisfies the condition of having exactly one line of reflectional symmetry.
2. Use a compass to draw a circle centered at \(P\) with radius equal to the length of \(\overline{PA}\) or \(\overline{PT}\), mark points \(A\) and \(T\) on the circle. The line - segment \(\overline{TA}\) is the chord and the shorter arc between \(T\) and \(A\) is the minor arc \(\widehat{TA}\).