Question

Write a two-column proof. Given: Triangle ACD is isosceles; <1 is congruent to <3 Prove: Segment AB || Segment CD

Answer 1

Answer:

AB ║ CD, reason If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel

Step-by-step explanation:

Statement,                                      Reason

Triangle ACD is isosceles,             Given

∠1 ≅ ∠3,                                           Given

∠3 ≅ ∠4,                                          Base angles of isosceles triangle

∠1 ≅ ∠4,                                           Substitution

∠1 and ∠4, are alt int. ∠s,                Definition

AB ║ CD,                                          Have congruent alternate interior angles

If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel