Question

word bank: definition of midpoint, reflexive property, definition of bisector, given, ∠cta ≅ ∠ads, ∠sad ≅ ∠tac, cpctc, sas, asa, sss, aas, hl, ∠s ≅ ∠t, (overline{ad}congoverline{ac}), prove, congruent. complete the following proof. use the word bank above to guide you. not all words will be used! given: ∠s≅∠t, (overline{sa}congoverline{at}) prove: △sad ≅ △tac. statements, reasons, 26., given, (overline{sa}congoverline{at}), 27., 28., vertical angles are congruent, △sad ≅ △tac, 29.

Explanation:

Step1: Identify given statements

The first given statement is $\angle S\cong\angle T$. So, for statement 26, it is $\angle S\cong\angle T$.

Step2: Identify reason for $SA\cong AT$

The reason for $SA\cong AT$ is that it is given. So, for 27, the reason is Given.

Step3: Identify vertical - angle congruence

The vertical - angle congruence is $\angle SAT\cong\angle TAS$ (but usually we just use the general fact of vertical angles are congruent). In the context of our proof for statement 28, it is $\angle SAT\cong\angle TAS$.

Step4: Determine congruence criterion

We have $\angle S\cong\angle T$, $SA\cong AT$, and $\angle SAT\cong\angle TAS$. By the ASA (Angle - Side - Angle) congruence criterion, $\triangle SAD\cong\triangle TAC$. So, for 29, the reason is ASA.

Answer:

1. $\angle S\cong\angle T$
2. Given
3. $\angle SAT\cong\angle TAS$
4. ASA