Question

△qsu is equilateral. complete the proof that △stu ≅ △srq.

(image of triangles rqt and qsu with intersection at s)

statement	reason
2. ∠rqs ≅ ∠sut	given
3. ∠tsu ≅ ∠qsr	vertical angle theorem
4. ( overline{su} cong overline{qs} )	definition of equilateral triangle
5. △stu ≅ △srq

Explanation:

Step1: Identify congruent angles

We have $\angle RQS \cong \angle SUT$ (Given) and $\angle TSU \cong \angle QSR$ (Vertical Angle Theorem).

Step2: Identify congruent side

$\overline{SU} \cong \overline{QS}$ (Definition of equilateral triangle).

Step3: Apply congruence postulate

The two pairs of congruent angles surround the congruent side, so by the ASA Congruence Postulate, $\triangle STU \cong \triangle SRQ$.

Answer:

Angle-Side-Angle (ASA) Congruence Postulate