Question

triangle congruence: sas
proving triangles congruent

1. c is the midpoint of \\( \overline { b d } \\)
2. \\( b c \cong c d \\)
3. \\( a c \cong a c \\)
4. \\( \angle b c a \\) and \\( \angle d c a \\) are right \\( \angle s \\)
5. \\( \cdot \\)
6. \\( \triangle a c b \cong \triangle a c d \\)
7. given
8. \\( \cdot \\)
9. reflexive property
10. given
11. all right \\( \angle s \\) are \\( \cong \\)
12. sas

given: c is the midpoint of \\( \overline { b d } \\).
prove: \\( \triangle a c b \cong \triangle a c d \\)
complete the two - column proof.
segment ac is perpendicular to segment bd
angles bca and dca form a linear pair
angle bca is congruent to angle dca

Explanation:

Step1: Recall the definition of midpoint

A midpoint of a segment divides the segment into two congruent segments.

Step2: Apply the definition to the given problem

Since $C$ is the midpoint of $\overline{BD}$, by the definition of midpoint, $BC\cong CD$.

Answer:

1. $BC\cong CD$; 2. definition of midpoint