Question

Which reason completes the proof below?

Given: ABCD is a parallelogram. ModifyingAbove upper A upper C with bar bisects Angle B C D and Angle B C D.

Prove: ABCD is a rhombus.
A. Opposite sides of a parallelogram are congruent.
B. Sides of a rhombus are congruent.
C. Diagonals of a parallelogram bisect each other.
D. Diagonals of a rectangle are congruent.

Answer 1

Observe the figure given.

Given: ABCD is a parallelogram.

To prove: ABCD is a rhombus

Statement

1. ABCD is a parallelogram. AC bisects $\angle BCD, \angle BAD$.

Reason: Given

2. $\angle 1 \cong \angle 2, \angle 3 \cong \angle 4$

Reason: Definition of an angle bisector

3. $AC \cong AC$

Reason: Reflexive property of congruence

4. $\Delta ABC \cong \Delta ADC$

Reason: ASA Postulate

5. $AB \cong AD, BC \cong DC$

Reason: corresponding parts of congruent triangles are equal.

6. $AB \cong CD, BC \cong AD$

Reason: Opposite sides of the parallelogram are congruent.

7. $AB \cong AD \cong BC \cong CD$

Reason: Transitive property of congruence

8. ABCD is a rhombus

Reason: Definition of rhombus

Answer 2

Answer: opposite sides of a parallelogram are congruent

Step-by-step explanation: