△pqs is equilateral, $ \overline { p t } \cong \overline { q r } $, and $ \angle s p t \cong \angle r q s $. complete the proof that $ \triangle q r s \cong \triangle p t s $.

1 △pqs is equilateral
2 $ \overline { p t } \cong \overline { q r } $
3 $ \angle s p t \cong \angle r q s $
4 $ \overline { p s } \cong \overline { q s } $
5 $ \triangle q r s \cong \triangle p t s $

Question

△pqs is equilateral, $ \overline { p t } \cong \overline { q r } $, and $ \angle s p t \cong \angle r q s $. complete the proof that $ \triangle q r s \cong \triangle p t s $.

1 △pqs is equilateral
2 $ \overline { p t } \cong \overline { q r } $
3 $ \angle s p t \cong \angle r q s $
4 $ \overline { p s } \cong \overline { q s } $
5 $ \triangle q r s \cong \triangle p t s $

Accepted Answer

# Explanation:
## Step1: Recall properties of equilateral triangle
An equilateral triangle has all sides congruent. Since $\triangle PQS$ is equilateral, by the definition of an equilateral triangle, all its sides are equal. So, $PS = QS$.
## Step2: Use SAS (Side - Angle - Side) congruence criterion
We are given $PT\cong QR$ ($side$), $\angle SPT\cong\angle RQS$ ($angle$), and from step 1 $PS\cong QS$ ($side$).

# Answer:
The reason for $PS\cong QS$ is "Definition of equilateral triangle".

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QUESTION IMAGE

Question

Explanation:

Step1: Recall properties of equilateral triangle

Step2: Use SAS (Side - Angle - Side) congruence criterion

Answer: