Question

move the statements into the table to complete the proof that the base angles of an isosceles triangle are congruent. given q is the mid - point of rt given definition of a midpoint reflexive property side - side - side postulate corresponding angles qs≅qs rs≅ts rq≅tq ∠srq≅∠stq △rsq≅△tsq

Explanation:

Step1: Identify given side - equality

$\overline{RS}\cong\overline{TS}$ is given (since we are dealing with an isosceles triangle, this is the property of an isosceles triangle where the two non - base sides are congruent).

Step2: Use mid - point property

Since $Q$ is the mid - point of $\overline{RT}$ (given), by the definition of a mid - point, $\overline{RQ}\cong\overline{TQ}$.

Step3: Apply reflexive property

$\overline{QS}\cong\overline{QS}$ by the reflexive property.

Step4: Prove triangle congruence

By the Side - Side - Side (SSS) Postulate, since $\overline{RS}\cong\overline{TS}$, $\overline{RQ}\cong\overline{TQ}$, and $\overline{QS}\cong\overline{QS}$, we have $\triangle RSQ\cong\triangle TSQ$.

Step5: Find congruent base angles

Since $\triangle RSQ\cong\triangle TSQ$, by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC), $\angle SRQ\cong\angle STQ$ (the base angles of the isosceles triangle).

Answer:

Statement	Reason
$Q$ is the mid - point of $\overline{RT}$	Given
$\overline{RQ}\cong\overline{TQ}$	Definition of a mid - point
$\overline{QS}\cong\overline{QS}$	Reflexive property
$\triangle RSQ\cong\triangle TSQ$	Side - Side - Side Postulate
$\angle SRQ\cong\angle STQ$	Corresponding angles (CPCTC)