Question

in circle t, ∠ptq ≅ ∠rts. what is the length of \\(\overline{pq}\\)? 4 units 7 units 6 units 3 units

Explanation:

Step1: Identify Congruent Triangles

Since \( \angle PTQ \cong \angle RTS \), and \( PT = RT \), \( QT = ST \) (radii of the circle), triangles \( PTQ \) and \( RTS \) are congruent by SAS (Side - Angle - Side) congruence criterion.

Step2: Corresponding Parts of Congruent Triangles

In congruent triangles, corresponding sides are equal. So, the length of \( \overline{PQ} \) should be equal to the length of \( \overline{RS} \). From the diagram, the length of \( \overline{RS} \) is 4 units.

Answer:

4 units