Subjects geometry

Triangle Congruency 6B33Cf

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1. **State the problem:** We are given that T is the midpoint of segment $\overline{WR}$ and two triangles $\triangle AWT$ and $\triangle ETR$ with certain congruent sides. We need to write the triangle congruency statement. 2. **Given:** $T$ is the midpoint of $\overline{WR}$, so $\overline{WT} \cong \overline{TR}$. 3. **Identify congruent sides:** From the problem, $\overline{AT} \cong \overline{TE}$ and $\overline{AW} \cong \overline{ER}$. 4. **Write the congruency statement:** Using the Side-Side-Side (SSS) congruence postulate, since all three pairs of corresponding sides are congruent, the triangles are congruent. 5. **Answer:** a. $\overline{WT} \cong \overline{TR}$ (because T is midpoint) b. $\triangle AWT \cong \triangle ETR$ c. Corresponding angles and sides of these triangles are congruent by SSS postulate. This completes the triangle congruency statement based on the given information.