Question

δrst and δpqt are equilateral. complete the proof that δpst ≅ δqrt.
statement reason
1 δrst is equilateral
2 δpqt is equilateral
3 (overline{rt}congoverline{st})
4 (overline{pt}congoverline{qt})
5 (angle ptscongangle qtr)
6 δpst ≅ δqrt

Explanation:

Step1: Given information

Given

Step2: Given information

Given

Step3: Definition of equilateral triangle

In equilateral $\triangle RST$, all sides are equal, so $\overline{RT}\cong\overline{ST}$

Step4: Definition of equilateral triangle

In equilateral $\triangle PQT$, all sides are equal, so $\overline{PT}\cong\overline{QT}$

Step5: Vertical - angles are congruent

$\angle PTS$ and $\angle QTR$ are vertical angles, so $\angle PTS\cong\angle QTR$

Step6: Side - Angle - Side (SAS) congruence criterion

Since $\overline{PT}\cong\overline{QT}$, $\angle PTS\cong\angle QTR$, $\overline{ST}\cong\overline{RT}$, by SAS, $\triangle PST\cong\triangle QRT$

Answer:

1. Given
2. Given
3. Sides of equilateral triangle are equal
4. Sides of equilateral triangle are equal
5. Vertical angles are congruent
6. SAS (Side - Angle - Side)