Question

1. Write a two-column proof.

Given: Triangle ACD is isosceles; <1 is congruent to <3

Prove: Segment AB || Segment CD

Answer 1

Check it below, please

Explanation:

Hi there!

Let's prove segment AB is perpendicular to CD. Attention to the fact that a two column proof has to be concise. So all the comments can't be exhaustive, but as short as possible.

Let's recap: An isosceles triangle is one triangle with at least 2 congruent angles.

Statement Reason

`\overline{AB} \cong \overline{AC}\\` Given

`\widehat{ACB} \:bisects\: \overline{AB}` Isosceles Triangle the altitude, the bisector coincide.

`\overline{AD} \cong \overline{DB}` Bisector equally divide a line segment into two congruent

`m\angle CDA =m \angle CBD=90^(\circ)` Right angles, perpendicular lines.

`\overline{CD}\perp \overline{AB}` Perpendicular Line segment