Question

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem. Angles PBC and BAD are congruent by the Corresponding Angles Theorem. By the __________ Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the Alternate Interior Theorem. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the __________ Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.

What properties accurately complete the proof?

Addition
Transitive

Reflexive
Reflexive

Substitution
Reflexive

Transitive
Transitive

Answer 1

The properties of equality that accurately complete the proof are the Transitive Property of Equality twice.

The properties that accurately complete the proof are:

Transitive Property of Equality: This property states that if a = b and b = c, then a = c.

In this case, we have ∠BCD = ∠PBC (by the Alternate Interior Angles Theorem) and ∠PBC = ∠BAD (by the Corresponding Angles Theorem).

Therefore, by the Transitive Property of Equality, ∠BCD = ∠BAD.

Transitive Property of Equality: This property is used again to conclude that ∠ABC = ∠CDA.

We have ∠ABC = ∠BAT (by the Alternate Interior Angles Theorem) and ∠BAT = ∠CDA (by the Corresponding Angles Theorem).

Therefore, by the Transitive Property of Equality, ∠ABC = ∠CDA.

Thus, the properties of equality that accurately complete the proof are the Transitive Property of Equality twice.

Answer 2

something goes wrong with the question:
" segment AB is parallel to segment DC and segment BC is parallel to segment AD" that is impossible when figure is built.