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

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

akposevictor akposevictor · Answer 2 · 2021-12-17T18:22:31+01:00

The two-column proof that shows that Segment AB║Segment CD is shown in the image attached below (See attachment).

Given the image showing an isosceles triangle, ΔACD.

The two-column proof that shows segment AB || Segment CD has been provided in the table shown in the image attached below.

We know already that:

ΔACD is isosceles

∠1 ≅ ∠3

∠3 and ∠4 base angles of the isosceles triangle, therefore, ∠3 ≅ ∠4.

By substitution, ∠1 ≅ ∠4

∠1 and ∠4 are alternate interior angles, therefore, based on the Converse of Alternate Interior Angles Theorem: AB║CD

The complete two-column proof is in the image attached below.

Learn more about Alternate Interior Angles Theorem on:

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