Question

Given: Triangle ACD is isosceles; <1 is congruent to <3 Prove: Segment AB || Segment CD

Answer 1

To prove that segment AB is parallel to segment CD, we can use the given information that triangle ACD is isosceles and angle 1 is congruent to angle 3.

Step-by-step explanation:

To prove that segment AB is parallel to segment CD, we can use the given information that triangle ACD is isosceles and angle 1 is congruent to angle 3. Let's break down the proof into steps:

1. Triangle ACD is isosceles, so we have AC = CD.
2. Angles 1 and 3 are congruent, so we have angle 1 = angle 3.
3. By the isosceles triangle theorem, the base angles of an isosceles triangle are congruent, so angle 1 = angle 2.
4. Since angle 1 = angle 2 and angle 1 = angle 3, we can conclude that angle 2 = angle 3.
5. By the alternate interior angles theorem, if two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. In this case, segments AB and CD are cut by transversal AD, and angle 2 = angle 3, so segments AB and CD are parallel.

Therefore, we have proven that segment AB is parallel to segment CD.

Answer 2

Segment AB || Segment CD

Step-by-step explanation:

Two lines are said to be parallel (||) if they do not meet, even when extended to infinity.

Given: <1 ≅ <3, ΔACD is an isosceles triangle.

Proof: Segment AB || Segment CD

From the diagram given,

AC ≅ AD (side property of isosceles triangle)

<3 = <4 (base angle property of an isosceles triangle)

<1 = <4 (alternate angle property)

Therefore, segment AB is parallel to segment CD.