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

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:

link

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

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: