Triangle Congruence 76964F

1. **Problem statement:** Given that triangle $ABC$ is congruent to triangle $BDE$, with $AB=15$ cm, $AC=13$ cm, and $DE=8$ cm, find: (i) length of $BC$ (ii) length of $CD$ (b) Complete the statement about angle $ACD$. 2. **Important rule:** Congruent triangles have corresponding sides and angles equal. Since $\triangle ABC \cong \triangle BDE$, corresponding sides are equal: $AB = BD$, $BC = DE$, $AC = BE$ and corresponding angles are equal. 3. **Step (a)(i): Find $BC$** Since $BC$ corresponds to $DE$ in the congruent triangles, and $DE=8$ cm, $$BC = DE = 8 \text{ cm}$$ 4. **Step (a)(ii): Find $CD$** Points $B$, $C$, and $D$ lie on the same segment $BD$. Since $BD = AB = 15$ cm (from congruence), and $BC = 8$ cm (from above), $$CD = BD - BC = 15 - 8 = 7 \text{ cm}$$ 5. **Step (b): Complete the statement about angle $ACD$** Angle $ACD$ corresponds to angle $BDE$ because $C$ corresponds to $D$ and $A$ corresponds to $B$ in the congruent triangles. Since $\angle BDE = 95^\circ$ (given), $$\angle ACD = 95^\circ$$ This is because corresponding angles of congruent triangles are equal. **Final answers:** (i) $BC = 8$ cm (ii) $CD = 7$ cm (b) $\angle ACD = 95^\circ$ because corresponding angles of congruent triangles are equal.