Question

use the side - angle - side triangle congruence theorem in a proof. supplies: straightedge tool, pencil, tracing paper warm up: information overload? highlight each piece of given information that is used in the proof, and each line in the proof where that piece of information is used. given: $overline{ab}congoverline{de}$, $angle acongangle d$, $overline{ac}congoverline{df}$, $angle bcongangle e$, $overline{bc}congoverline{ef}$, $angle ccongangle f$

Explanation:

Step1: Recall SAS congruence theorem

The SAS (Side - Angle - Side) Triangle Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify relevant given information

We need two pairs of congruent sides and the included congruent angle. Given $\overline{AB}\cong\overline{DE}$, $\overline{AC}\cong\overline{DF}$ and $\angle A\cong\angle D$. Here, $\angle A$ is the included angle between $\overline{AB}$ and $\overline{AC}$ in $\triangle ABC$, and $\angle D$ is the included angle between $\overline{DE}$ and $\overline{DF}$ in $\triangle DEF$.

Step3: Highlight the used information

We highlight $\overline{AB}\cong\overline{DE}$, $\overline{AC}\cong\overline{DF}$ and $\angle A\cong\angle D$ as the pieces of given information used in the proof. In the proof steps where we apply the SAS theorem, we refer to these congruences.

Answer:

Highlight $\overline{AB}\cong\overline{DE}$, $\overline{AC}\cong\overline{DF}$, $\angle A\cong\angle D$ and the lines in the proof where these congruences are used to show $\triangle ABC\cong\triangle DEF$ by SAS.