Question

select the correct answer from each drop - down menu.
given: rhombus (abcd) with diagonal (overline{ac})
prove: (overline{ac}) bisects (angle dab) and (angle bcd)
identify the missing statement and reason in the proof.
given rhombus (abcd) with diagonal (overline{ac}), it follows from the definition of a rhombus that (overline{ab}congoverline{bc}congoverline{cd}congoverline{ad}). by the reflexive property of congruence, (overline{ac}congoverline{ac}). so, (\triangle daccong\triangle bac) by the (\boldsymbol{downarrow}). since corresponding parts of congruent triangles are congruent, (angle daccong\boldsymbol{downarrow}) and (angle dcacong\boldsymbol{downarrow}). so, by the definition of segment bisector (overline{ac}) bisects (angle dab) and (angle bcd).
(there is an image of rhombus (abcd) with diagonal (ac) drawn, and buttons reset and next at the bottom left.)

Explanation:

Step1: Identify triangle congruence criterion

In rhombus \(ABCD\), \(AB \cong AD\) (sides of a rhombus are congruent), \(AC\) is common (reflexive property), and \(AD \cong AB\) (rhombus sides). So \(\triangle DAC \cong \triangle BAC\) by \(SSS\) (Side - Side - Side) congruence criterion.

Step2: Find corresponding congruent angles

Since \(\triangle DAC \cong \triangle BAC\), the corresponding angles \(\angle DAC \cong \angle BAC\) (first missing angle: \(\angle BAC\)) and \(\angle DCA \cong \angle BCA\) (second missing angle: \(\angle BCA\)).

Answer:

• First drop - down (angle congruent to \(\angle DAC\)): \(\angle BAC\)
• Congruence criterion: \(SSS\) (Side - Side - Side)
• Second drop - down (angle congruent to \(\angle DCA\)): \(\angle BCA\)