Question

PLEASE HELP ITS DUe In 5MINUTES

Answer 1

The complete statement and reasons proving the sides
`\overline{AB}` and
`\overline{CD}` are congruent,
`\overline{AB}` ≅
`\overline{CD}`, can be presented as follows;

Step Statement Reason

1 ∠B ≅ ∠D,
`\overline{BC}` ║
`\overline{AD}` Given

2. ∠BCA ≅ ∠DAC Parallel lines cut by a transversal

form congruent alt. Int. angles

3.
`\overline{AC}` ≅
`\overline{AC}` Reflexive Property

4. ΔABC ≅ ΔCDA ASA Congruence Rule

5.
`\overline{AB}` ≅
`\overline{CD}` CPCTC

What are congruent segments; Congruent segments are segments that have the same size.

The details for the reason used to prove the sides
`\overline{AB}` and
`\overline{CD}` are congruent are as follows;

Parallel sides cut by a transversal form form congruent alternate interior angles

The alternate interior angles theorem states that, the alternate interior angles formed at the alternate sides of a transversal on the inside of the parallel lines are congruent

Reflexive property

The reflexive property states that a segment, angle or figure is congruent to itself

ASA Congruence rule

The Angle-Side-Angle, ASA congruence rule states that of two angles and an included side in one triangle, are congruent to two angles and an included side of another triangle, then the two triangles are congruent