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
∴ [tex]\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}[/tex]
∵ AD = 8 feet
∵ DB = 2 feet
∴ AB = AD + DB
∴ AB = 8 + 2 = 10 feet
∵ AE = 4 feet
By using the proportion statement above [tex]\frac{AD}{AB}=\frac{AE}{AC}[/tex]
∴ [tex]\frac{8}{10}=\frac{4}{AC}[/tex]
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
