Question

If segments DE and AB are parallel, which of the following expressions will help determine the length of segment AC?

A. AC=AD+DC

B. AC=AE+EC

C. AC=AD−DC

D. AC=AE−EC

Answer 1

The expression that will help determine the length of segment AC when segments DE and AB are parallel is AC = AD + DC. Hence the correct answer is option A

Step-by-step explanation:

The expression that will help determine the length of segment AC when segments DE and AB are parallel is AC = AD + DC.

When DE and AB are parallel, the two segments form a transversal. According to the properties of parallel lines, the corresponding angles are congruent, which means that angle DCA is equal to angle ECD. This implies that segments AD and DC are equal in length, leading to the expression AC = AD + DC.

For example, if AD = 5 units and DC = 3 units, then the length of segment AC would be 5 + 3 = 8 units.

Hence the correct answer is option A