Question

Camden is creating a model of a pyramid. The model created will need to be scaled up from the blueprint.

If segments DE and AB are parallel, which of the following expressions will help Camden determine the length of DC?
DC equals EC times AC all over BC
DC = EC
DC equals EC times AC all over AB
DC = AB

Answer 1

DC equals EC times AC all over BC

Explanation:

Answer 2

A) DC equals EC times AC all over BC.

Explanation:

We know that:

`DE\parallel AB`

Then by corresponding angles:

`\angle CAB\cong \angle CDE\text{ and } \angle CBA\cong \angle CED`

So, by AA-Similarity:

`\Delta CDE\sim \Delta CAB`

Corresponding sides of similar triangles are in proportion. Hence:

`\displaystyle (DC)/(AC)=(EC)/(BC)`

By multiplying both sides by AC:

`\displaystyle DC=(EC\cdot AC)/(BC)`

DC is equal to EC times AC over BC.

Hence, our answer is A.