Question

t is the midpoint of $overline{qs}$ and $overline{pr}$. complete the proof that $delta pst cong delta rqt$.

statement

reason

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1

$t$ is the midpoint of $overline{qs}$

given

2

$t$ is the midpoint of $overline{pr}$

given

3

$overline{ps} cong overline{qr}$

given

4

$overline{qt} cong overline{st}$

definition of midpoint

5

$overline{pt} cong overline{rt}$

definition of midpoint

6

$delta pst cong delta rqt$

Explanation:

Step1: Identify given congruent sides

1. $\overline{PS} \cong \overline{QR}$ (Given)
2. $\overline{QT} \cong \overline{ST}$ (Definition of midpoint)
3. $\overline{PT} \cong \overline{RT}$ (Definition of midpoint)

Step2: Match congruence criterion

We have three pairs of corresponding sides of $\triangle PST$ and $\triangle RQT$ that are congruent. This satisfies the Side-Side-Side (SSS) triangle congruence postulate.

Answer:

Side-Side-Side (SSS) Congruence Postulate