Question

50 POINTS URGENT PLEASE ANSWER ASAP
The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:
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According to the given information, line AB || line DC and line BC || line AD. Construct a diagonal from A to C with a straightedge. It is congruent to itself by the Reflexive Property of Equality.
Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the Alternate Interior Theorem. _____
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CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.
Which sentence accurately completes the proof?


(A) Triangles BCA and DAC are congruent according to the Angle-Angle-Side (AAS) Theorem.

(B)Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.

(C)Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles are congruent).

(D)Angles BAD and ADC, as well as angles DCB and CBA, are supplementary by the Same-Side Interior Angles Theorem

Answer 1

Answer:

The correct option is;

(B) Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.

Step-by-step explanation:

The given information are;

Lines AB and BC are parallel lines DC and AD respectively

AC constructed is congruent to AC (Reflexive property of equality)

∠BAC ≅ ∠DCA (Alternate angles theorem)

∠BCA ≅ ∠DAC (Alternate angles theorem)

Therefore, we have;

Triangle ΔBCA and triangle ΔDAC are congruent by Angle-Side-Angle (ASA) Theorem because, the congruent angles between ΔBCA and ΔDAC which are (∠BAC, ∠BCA in ΔBCA and ∠DCA and ∠DAC in ΔDAC) ∠BAC ≅ ∠DCA and ∠BCA ≅ ∠DAC are on opposite ends of the congruent line AC between the two triangles, therefore, we use the ASA Theorem