Question

1. ( mangle acd = 90^{circ} ) and ( angle acbcongangle acd ) 3. all right angles are congruent 4. ( overline{bc}congoverline{dc} ) 4. definition of midpoint 5. ( overline{ac}congoverline{ac} ) 5. reflexive property 6. ( \triangle acbcong\triangle acd ) 6. 7. ( overline{ab}congoverline{ad} ) 7. a line 6: side - angle - side line 7: corresponding parts of congruent triangles are congruent b line 6: angle - side - angle line 7: corresponding parts of congruent triangles are congruent c line 6: side - side - side line 7: corresponding parts of similar triangles are congruent d line 6: side - angle - side line 7: corresponding parts of similar triangles are congruent

Explanation:

• For line 6: We have two sides ($\overline{BC}\cong\overline{DC}$, $\overline{AC}\cong\overline{AC}$) and the included angle ($\angle ACB\cong\angle ACD$) which satisfies the Side - Angle - Side (SAS) congruence criterion.
• For line 7: When two triangles ($\triangle ACB$ and $\triangle ACD$) are congruent, their corresponding parts (in this case $\overline{AB}$ and $\overline{AD}$) are congruent. This is known as Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

Answer:

A. Line 6: Side - Angle - Side; Line 7: Corresponding parts of congruent triangles are congruent