Question

Please assist, quickyl!

Answer 1

`2. \ \mathrm{alternate\ interior\ 4.\ AC=AC[Common\ side]}`

Answer 2

Reason 2: Alternate interior

Statement 4: AC = CA

Reason 4: They are lengths of the same segment.

Explanation:

Statement 2

`\angle 2 \cong \angle 4`

Reason 2

A transversal is a line that intersects two or more parallel lines. When a transversal intersects a pair of parallel lines, it creates several angles.

In the given parallelogram ABCD, line segment AC is the transversal. It intersects both pairs of parallel lines.

Alternate interior angles are a pair of angles that are on opposite sides of the transversal and inside (between) the two parallel lines.

In the given parallelogram ABCD, angles 1 and 3 are on opposite sides of the transversal and inside the parallel lines. Similarly, angles 2 and 4 are on opposite sides of the transversal and inside the parallel lines.

According to the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then the alternate interior angles are equal.

Therefore, we can use the Alternate Interior Angles Theorem to prove that angles 2 and 4 are congruent.

The correct reason for statement 2 is:

• When a transversal crosses parallel lines, alternate interior angles are congruent.

`\hrulefill`

Statement 4

AC = CA

Reason 4

From inspection of parallelogram ABCD, we can see that triangle ABC and triangle CDA share a common side: line segment AC.

The Reflexive Property of Congruence states that any line segment is congruent to itself.

Therefore, the correct reason for statement 4 is:

• They are lengths of the same segment.