Question

Jolene is creating a model of a pyramid. The model created will need to be scaled up from the blueprint. triangle ACB, point D is on segment AC between points A and C, point E is on segment BC between points B and C If segments DE and AB are parallel, which of the following expressions will help Jolene determine the length of segment AC? AC equals CB times CD all over CE AC = AB AC equals CB times AC all over CE AC = BC

Answer 1

Answer:

AC equals CB times CD all over CE

Answer 2

The lengths of the sides of the scaled drawing can be determined from the

relation between similar triangles.

The expression that will help Jolene determine the length segment AC is the option;

• $\displaystyle \underline{CD= \frac{CB\cdot CD}{CE}}$

Reasons:

The given parameters are;

The figure Jolene is trying to create = A scaled up blue print

Given that in ΔACB and ΔABC, we have;

DE and AB are parallel

Therefore;

∠CED ≅ ∠CBA by corresponding angles

∠CDE ≅ ∠CAB by corresponding angles

∠C ≅ ∠C by reflexive properties

ΔCDE ~ ΔACB by Angle-Angle similarity postulate

Therefore, by similar triangles, and triangle proportionality, we have;

$\displaystyle \frac{AC}{CD} = \mathbf{\frac{CB}{CE}}$

Therefore;

$\displaystyle CD= \mathbf{ \frac{CB\cdot CD}{CE}}$

Therefore, if segments DE and AB are parallel, the expression that will help Jolene determine the length segment AC is; $\displaystyle CD= \frac{CB\cdot CD}{CE}$

Learn more about similar triangles here:

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