Complete the two-column proof.
Statement | Reason
------------------------------------|-----------------------
1. \(\angle ABC\) and \(\angle CBD\) are both right angles. | Supplementary angles are congruent.
2. \(\angle ABC\) and \(\angle CBD\) are congruent. | Definition of right angles.
3. \(AD\) bisects \(\angle ABC\). | Definition of angle bisector.
4. \(\angle BAC \cong \angle CBD\). | Transitive property of congruence.
5. \(\triangle ABD\) is isosceles. | Definition of isosceles triangle.
6. \(AB \cong BD\). | Definition of isosceles triangle.
Given: alt="x over 6 plus 2 equals 15"
Prove: x = 78
alt="x over 6 plus 2 equals 15" a. __________
alt="x over 6 equals 13" b. __________
x = 78 c. __________
Given: \( \frac{x}{6} + 2 = 15 \)
Prove: \( x = 78 \)
Statement | Reason
--------------------------------|-----------------------
\( \frac{x}{6} + 2 = 15 \) | Given
\( \frac{x}{6} = 13 \) | Subtracting 2 from both sides
\( x = 78 \) | Multiplying both sides by 6