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 -- I will mark brainliest; If your response is inapropriate, or just a way to get points, it will get reported! Thank you so much !

Answer 1

The missing figure is attached down

Answer:

The measure of EC is 1 foot

Step-by-step explanation:

Let us revise the cases of similarity

• AAA similarity : two triangles are similar if all three angles in the first triangle equal the corresponding angle in the second triangle
• AA similarity : If two angles of one triangle are equal to the  corresponding angles of the other triangle, then the two triangles  are similar.
• SSS similarity : If the corresponding sides of the two triangles are  proportional, then the two triangles are similar.
• SAS similarity : In two triangles, if two sets of corresponding sides  are proportional and the included angles are equal then the two  triangles are similar.  

From the attached figure

∵ DE // BC

∴ ∠ADE ≅ ABC ⇒ corresponding angles

∴ ∠AED ≅ ACB ⇒ corresponding angles

In Δs ADE and ABC

∵ ∠ADE ≅ ABC ⇒ proved

∵ ∠AED ≅ ACB ⇒ proved

∵ ∠A is a common angle in the two triangles

∴ Δ ADE is similar to triangle ABC by AAA postulate

From the results of similarity the corresponding sides of the triangles are proportion

∴ $\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}$

∵ AD = 8 feet

∵ DB = 2 feet

∴ AB = AD + DB

∴ AB = 8 + 2 = 10 feet

∵ AE = 4 feet

By using the proportion statement above  $\frac{AD}{AB}=\frac{AE}{AC}$

∴ $\frac{8}{10}=\frac{4}{AC}$

By using cross multiplication

∴ 8 × AC = 10 × 4

∴ 8 AC = 40

Divide both sides by 8

∴ AC = 5 feet

∵ AC = AE + EC

∴ 5 = 4 + EC

Subtract 4 from both sides

∴ 1 = EC

∴ The measure of EC is 1 foot