Question

Justify each statement with a property from algebra or property of congruence.

If $\overline{\mathrm{AB}}\cong \overline{\mathrm{CD}}$and $\overline{\mathrm{DC}}\cong \overline{\mathrm{EP}}$then $\overline{\mathrm{AB}}\cong \overline{\mathrm{EP}}$.

Short answer

From the property of congruence, it is proved that $\overline{AB}\cong \overline{EF}$.

Step-by-step solution

Step 1. Transitive property of congruence.

If$\overline{PQ}\cong \overline{MN}$ and $\overline{MN}\cong \overline{RS}$then $\overline{PQ}\cong \overline{RS}$.

Step 2. Apply the property.

Apply transitive property of congruence to the given sides, that is, to the sides, $\overline{AB}$, $\overline{CD}$and$\overline{EF}$.

Step 3. Apply the property.

Therefore, $\overline{AB}\cong \overline{CD}$,$\overline{CD}\cong \overline{EF}$gives $\overline{AB}\cong \overline{EF}$.