Question

In the image below, DE ∥ BC. Find the measure of EC. Set up a proportion and solve for the measure. Show your work and label your answer. PLEASE HELP ME !!

Answer 1

Answer:

EC = 1 ft

Step-by-step explanation:

DE // BC and AC and AD are transversal lines

∴ ∠E≅∠C  ⇒ corresponding angles are congruent

  ∠D≅∠B  ⇒ corresponding angles are congruent

 ∠A≅∠A   ⇒ Reflexive property

∴Δ ADE is similar to ΔABC  by AA postulate

So, The corresponding sides are in proportion.

$\frac{AC}{AE} = \frac{AB}{AD}$

AE = 4 ft , AD = 8 ft , AB = 8 + 2 = 10 ft

AC = AE * AB/AD = 4*10/8 = 40/8 = 5 ft

EC = AC - AE = 5 - 4 = 1 ft

So, the Length of EC = 1 ft.